首页 分数的速算与巧算

分数的速算与巧算

举报
开通vip

分数的速算与巧算 ߚߚ᭄ⱘ䗳ㅫϢᎻㅫ� 1ǃ 㺖乍˖ᰃ䅵ㅫЁ䳔㽕থ⦄㾘ᕟǃ߽⫼݀ᓣⱘ䖛⿟ˈ㺖乍Ϣ䗮乍ᔦ㒇ᰃᆚϡৃߚⱘˈᴀ䆆㽕∖ᄺ⫳ᥠᦵ 㺖乍ᡔᎻঞᇏᡒ䗮乍䖯㸠㾷乬ⱘ㛑࡯� 2ǃ ᤶܗ˖䅽ᄺ⫳㛑໳ᥠᦵㄝ䞣ҷᤶⱘὖᗉˈ䗮䖛ㄝ䞣ҷᤶ䆆໡ᴖㅫᓣব៤ㅔऩㅫᓣDŽ� 3ǃ ᕾ⦃ᇣ᭄Ϣߚ᭄ᢚߚ˖ᥠᦵᕾ⦃ᇣ᭄Ϣߚ᭄ⱘѦ࣪ˈᕾ⦃ᇣ᭄П䯈ㅔऩⱘࡴǃޣ䖤ㅫˈ⍝ঞᕾ⦃ᇣ᭄ Ϣߚ᭄ⱘЏ㽕߽⫼䖤ㅫᅮᕟ䖯㸠ㅔㅫⱘ䯂乬ˊ� �ǃ䗮乍ᔦ㒇⊩� 䗮乍ᔦ㒇⊩г㽕׳ࡽѢҷ᭄ˈᇚㅫᓣ࣪ㅔˈԚᤶܗ⊩াᰃᇚĀᔶৠāⱘㅫᓣ⫼ᄫ↡ҷ᳓ᑊখϢ䅵ㅫˈ Փ䅵ㅫ䖛⿟᳈ࡴㅔ֓...

分数的速算与巧算
ߚߚ᭄ⱘ䗳ㅫϢᎻㅫ� 1ǃ 㺖乍˖ᰃ䅵ㅫЁ䳔㽕থ⦄㾘ᕟǃ߽⫼݀ᓣⱘ䖛⿟ˈ㺖乍Ϣ䗮乍ᔦ㒇ᰃᆚϡৃߚⱘˈᴀ䆆㽕∖ᄺ⫳ᥠᦵ 㺖乍ᡔᎻঞᇏᡒ䗮乍䖯㸠㾷乬ⱘ㛑࡯� 2ǃ ᤶܗ˖䅽ᄺ⫳㛑໳ᥠᦵㄝ䞣ҷᤶⱘὖᗉˈ䗮䖛ㄝ䞣ҷᤶ䆆໡ᴖㅫᓣব៤ㅔऩㅫᓣDŽ� 3ǃ ᕾ⦃ᇣ᭄Ϣߚ᭄ᢚߚ˖ᥠᦵᕾ⦃ᇣ᭄Ϣߚ᭄ⱘѦ࣪ˈᕾ⦃ᇣ᭄П䯈ㅔऩⱘࡴǃޣ䖤ㅫˈ⍝ঞᕾ⦃ᇣ᭄ Ϣߚ᭄ⱘЏ㽕߽⫼䖤ㅫᅮᕟ䖯㸠ㅔㅫⱘ䯂乬ˊ� �ǃ䗮乍ᔦ㒇⊩� 䗮乍ᔦ㒇⊩г㽕׳ࡽѢҷ᭄ˈᇚㅫᓣ࣪ㅔˈԚᤶܗ⊩াᰃᇚĀᔶৠāⱘㅫᓣ⫼ᄫ↡ҷ᳓ᑊখϢ䅵ㅫˈ Փ䅵ㅫ䖛⿟᳈ࡴㅔ֓ˈ㗠䗮乍ᔦ㒇⊩㛑ᇚĀᔶԐāⱘ໡ᴖㅫᓣˈ⫼ᄫ↡㸼⼎ৢ࣪ㅔЎᐌ㾕ⱘϔ㠀ᔶᓣˊ� ⶹ䆚⚍ᢼ� ϔǃ㺖乍㓐ড়� ˄ϔ ǃ˅Ā㺖Ꮒāൟ䖤ㅫ� ���ᇍѢߚ↡ৃҹݭ԰ϸϾ಴᭄Ь⿃ⱘߚ᭄ˈे 1 a bu ᔶᓣⱘˈ䖭䞠៥Ӏᡞ䕗ᇣⱘ᭄ݭ೼ࠡ䴶ˈे a b� ˈ 䙷М᳝ 1 1 1 1( ) a b b a a b �u � � ���ᇍѢߚ↡ϞЎ �Ͼ៪ �Ͼ䖲㓁㞾✊᭄Ь⿃ᔶᓣⱘߚ᭄ˈे˖� 1 ( 1) ( 2)n n nu � u � ˈ 1 ( 1) ( 2) ( 3)n n n nu � u � u � ᔶᓣⱘˈ៥Ӏ᳝˖� 1 1 1 1[ ] ( 1) ( 2) 2 ( 1) ( 1)( 2)n n n n n n n �u � u � u � � � � 1 1 1 1[ ] ( 1) ( 2) ( 3) 3 ( 1) ( 2) ( 1) ( 2) ( 3)n n n n n n n n n n �u � u � u � u � u � � u � u � � 㺖Ꮒൟ㺖乍ⱘϝ໻݇䬂⡍ᕕ˖� ˄�˅ߚᄤܼ䚼Ⳍৠˈ᳔ㅔऩᔶᓣЎ䛑ᰃ �ⱘˈ໡ᴖᔶᓣৃЎ䛑ᰃ [�[Ўӏᛣ㞾✊᭄�ⱘˈԚᰃা㽕ᇚ [ ᦤপߎᴹेৃ䕀࣪Ўߚᄤ䛑ᰃ �ⱘ䖤ㅫDŽ� ˄�˅ߚ↡ϞഛЎ޴Ͼ㞾✊᭄ⱘЬ⿃ᔶᓣˈᑊϨ⒵䎇Ⳍ䚏 �Ͼߚ↡Ϟⱘ಴᭄Ā佪ሒⳌ᥹ā� ˄�˅ߚ↡Ϟ޴Ͼ಴᭄䯈ⱘᏂᰃϔϾᅮؐDŽ� ˄Ѡ ǃ˅Ā㺖੠āൟ䖤ㅫ˖� ᐌ㾕ⱘ㺖੠ൟ䖤ㅫЏ㽕᳝ҹϟϸ⾡ᔶᓣ˖� ˄�˅ 1 1a b a b a b a b a b b a � � �u u u �˄�˅ 2 2 2 2a b a b a b a b a b a b b a � � �u u u � 㺖੠ൟ䖤ㅫϢ㺖Ꮒൟ䖤ㅫⱘᇍ↨˖� 㺖Ꮒൟ䖤ㅫⱘḌᖗ⦃㡖ᰃĀϸϸᢉ⍜䖒ࠄㅔ࣪ⱘⳂⱘāˈ 㺖੠ൟ䖤ㅫⱘ乬Ⳃϡҙ᳝Āϸϸᢉ⍜āൟⱘˈ ৠᯊ䖬᳝䕀࣪ЎĀߚ᭄ޥᭈāൟⱘˈҹ䖒ࠄㅔ࣪ⳂⱘDŽ� ˄ϝ ǃ˅ᭈ᭄㺖乍� ����1 2 2 3 3 4 ... ( 1)n nu � u � u � � � u 1 ( 1) ( 1) 3 n n n � u u � � ���� 11 2 3 2 3 4 3 4 5 ... ( 2) ( 1) ( 2)( 1) ( 1) 4 n n n n n n nu u � u u � u u � � � u � u � � � � Ѡǃᤶܗ� 㾷᭄ᄺ乬ᯊ ᡞˈᶤϾᓣᄤⳟ៤ϔϾᭈԧ ⫼ˈ঺ϔϾ䞣এҷ᳓ᅗ Ңˈ㗠Փ䯂乬ᕫࠄㅔ࣪ˈ䖭িᤶܗ⊩ ᤶˊ ܗⱘᅲ䋼ᰃ䕀࣪ˈᇚ໡ᴖⱘᓣᄤ࣪㐕Ўㅔˊ� � ϝǃᕾ⦃ᇣ᭄࣪ߚ᭄� �ǃᕾ⦃ᇣ᭄࣪ߚ᭄㒧䆎˖� � 㒃ᕾ⦃ᇣ᭄� ⏋ᕾ⦃ᇣ᭄� ߚᄤ� ᕾ⦃㡖Ёⱘ᭄ᄫ᠔㒘៤ⱘ᭄� ᕾ⦃ᇣ᭄এᥝᇣ᭄⚍ৢⱘ᭄ᄫ᠔㒘៤ⱘ᭄Ϣϡᕾ⦃䚼ߚ᭄ᄫ᠔㒘៤ⱘ᭄ⱘᏂ� ߚ↡� QϾ �ˈ݊Ё QㄝѢᕾ⦃㡖᠔৿ⱘ᭄ᄫϾ᭄� ᣝᕾ⦃ԡ᭄⏏ �ˈϡᕾ⦃ԡ᭄⏏ �ˈ㒘៤ߚ↡ˈ݊Ё � ೼ �ⱘᎺջ� · 0. 9 aa ˗���� · ·0. 99 abab ˗���� · · 10.0 99 10 990 ab abab u ˗���� · ·0. 990 abc aabc � ˈĂĂ� ��ǃऩԡߚ᭄ⱘᢚߚ˖� ՟˖ 1 10 1 1 20 20 � � � � � 1 1� � � � � 1 1� � � � � 1 1� � � � � 1 1� � ߚᵤ˖ߚ᭄ऩԡⱘᢚߚˈЏ㽕ᮍ⊩ᰃ˖� Ңߚ↡ 1ⱘ㑺᭄ЁӏᛣᡒߎϸϾ P੠ Q�᳝˖� � � 1 1( ) ( ) ( ) ( ) m n m n N N m n N m n N m n � �� � � 1 1 A B � � ᴀ乬 ��ⱘ㑺᭄᳝����������DŽ� ՟བ˖䗝 �੠ �ˈ᳝˖� � � 1 1(1 2) 1 2 1 1 10 10(1 2) 10(1 2) 10(1 2) 30 15 � � �� � � � ᴀ乬݋ԧⱘ㾷᳝˖� � � 1 1 1 1 1 1 1 1 1 10 11 110 12 60 14 35 15 30 � � � � � ՟乬㊒䆆� ῵ഫϔǃߚߚ᭄㺖乍� Ǐ՟ 1ǐ� 1 1 1 1 1 1 2 3 4 2 3 4 5 3 4 5 6 6 7 8 9 7 8 9 10 � � � ˜˜ ˜ � �u u u u u u u u u u u u u u u �� ࠓࠓ๥๥€€��ॳᓣ 1 1 1 1 1 1 1 3 1 2 3 2 3 4 2 3 4 3 4 5 7 8 9 8 9 10 § · u � � � � � �¨ ¸u u u u u u u u u u u u© ¹" � 1 1 1 3 1 2 3 8 9 10 § · u �¨ ¸u u u u© ¹ 119 2160 � ٧٧څڅ€€�� 3 3 3...... 1 2 3 4 2 3 4 5 17 18 19 20 � � �u u u u u u u u u � ࠓࠓ๥๥€€��ॳᓣ 1 1 1 1 1 1 13 [ ( ... )] 3 1 2 3 2 3 4 2 3 4 3 4 5 17 18 19 18 19 20 u u � � � � � �u u u u u u u u u u u u � 1 1 3 19 20 1 1139 1 2 3 18 19 20 18 19 20 6840 u u � � u u u u u u � Ǐ՟ 2ǐ�䅵ㅫ˖ 5 7 19 1 2 3 2 3 4 8 9 10 � � � u u u u u u" ����������ˊ� ࠓࠓ๥๥€€��བᵰᓣᄤЁ↣ϔ乍ⱘߚᄤ䛑Ⳍৠˈ䙷Мህᰃϔ䘧ᕜᐌ㾕ⱘߚ᭄㺖乍ⱘ乬ⳂˊԚᰃᴀ乬Ёߚᄤϡ Ⳍৠˈ㗠ᰃ៤ㄝᏂ᭄߫ˈϨㄝᏂ᭄߫ⱘ݀ᏂЎ �ˊⳌ↨䕗Ѣ �ˈ�ˈ�ˈĂĂ䖭ϔ݀ᏂЎ �ⱘㄝᏂ ᭄߫�䆹᭄߫ⱘ㄀ nϾ᭄ᙄདЎ nⱘ �ס� ॳˈᓣЁߚᄤ᠔៤ⱘㄝᏂ᭄߫↣ϔ乍䛑↨݊໻ � ᠔ˈҹ ৃҹܜᡞॳᓣЁ↣ϔ乍ⱘߚᄤ䛑ߚ៤ �Ϣ঺ϔϾⱘ੠ݡ䖯㸠䅵ㅫˊ� ॳᓣ 3 2 3 4 3 16 1 2 3 2 3 4 8 9 10 � � � � � �u u u u u u" � 1 1 1 1 2 83 2 1 2 3 2 3 4 8 9 10 1 2 3 2 3 4 8 9 10 § · § · u � � � � u � � �¨ ¸ ¨ ¸u u u u u u u u u u u u© ¹ © ¹" " � 1 1 1 1 1 1 1 1 1 13 2 2 1 2 2 3 2 3 3 4 8 9 9 10 2 3 3 4 9 10 § · § · u u � � � � � � � u � � �¨ ¸ ¨ ¸u u u u u u u u u© ¹ © ¹" " � 3 1 1 1 1 1 1 1 12 2 1 2 9 10 2 3 3 4 9 10 § · § · u � � u � � � � � �¨ ¸ ¨ ¸u u© ¹ © ¹" � 3 1 1 1 12 2 2 90 2 10 § · § · u � � u �¨ ¸ ¨ ¸© ¹ © ¹ � 7 1 1 4 60 5 � � � 23 15 � гৃҹⳈ᥹䖯㸠䗮乍ᔦ㒇ˊḍ᥂ㄝᏂ᭄߫ⱘᗻ䋼ˈৃⶹߚᄤⱘ䗮乍݀ᓣЎ 2 3n � ˈ᠔ҹ � � � � � � � � � � � � 2 3 2 3 1 2 1 2 1 2 n n n n n n n n n � �u � u � � u � u � u � ˈ ݡ ᇚ ↣ ϔ 乍 ⱘ � � � � 2 1 2n n� u � Ϣ � � � � 3 1 2n n nu � u � ߚ߿ࡴ೼ϔ䍋䖯㸠㺖乍ˊৢ䴶ⱘ䖛⿟Ϣࠡ䴶ⱘᮍ⊩Ⳍ ৠˊ� ٧٧څڅ€€��䅵ㅫ˖ 5 7 17 191155 2 3 4 3 4 5 8 9 10 9 10 11 u � � � �u u u u u u u u"˄ �˅�������� ࠓࠓ๥๥€€��ᴀ乬ⱘ䞡⚍೼Ѣ䅵ㅫᣀোݙⱘㅫᓣ˖ 5 7 17 19 2 3 4 3 4 5 8 9 10 9 10 11 � � � �u u u u u u u u" ˊ䖭Ͼ ㅫᓣϡৠѢ៥Ӏᐌ㾕ⱘߚ᭄㺖乍ⱘഄᮍ೼Ѣ↣ϔ乍ⱘߚᄤձ⃵៤ㄝᏂ᭄߫ˈ㗠䴲ᐌ㾕ⱘߚᄤⳌ ৠǃ៪ߚᄤᰃߚ↡ⱘᏂ៪੠ⱘᚙމˊ᠔ҹᑨᔧᇍߚᄤ䖯㸠䗖ᔧⱘবᔶˈՓП䕀࣪៤៥Ӏ❳ᙝⱘ ᔶᓣˊ� 㾖ᆳৃⶹ 5 2 3 � ˈ 7 3 4 � ˈĂĂे↣ϔ乍ⱘߚᄤ䛑ㄝѢߚ↡ЁࠡϸϾЬ᭄ⱘ੠ˈ᠔ҹ� 5 7 17 19 2 3 4 3 4 5 8 9 10 9 10 11 � � � �u u u u u u u u" 2 3 3 4 9 10 2 3 4 3 4 5 9 10 11 � � � � � �u u u u u u" � � � � � 1 1 1 1 1 3 4 2 4 4 5 3 5 1 0 1 � � � � � �u u u u u" � 1 1 1 1 1 1 3 4 4 5 10 11 2 4 3 5 9 11 § · § · � � � � � � �¨ ¸ ¨ ¸u u u u u u© ¹ © ¹" " � 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 4 4 5 10 11 2 2 4 3 5 4 6 8 10 9 11 § · § · � � � � � � � u � � � � � � � � � �¨ ¸ ¨ ¸© ¹ © ¹" " � 1 1 1 1 1 1 1 3 11 2 2 10 3 11 § · § · � � u � � �¨ ¸ ¨ ¸© ¹ © ¹ 8 1 2 8 33 2 5 33 § · � u �¨ ¸© ¹ 31 55 � ᠔ҹॳᓣ 311155 651 55 u ˊ� ٧٧څڅ€€��䅵ㅫ˖ 3 4 5 12 1 2 4 5 2 3 5 6 3 4 6 7 10 11 13 14 � � � �u u u u u u u u u u u u" �� ࠓࠓ๥๥€€��㾖ᆳৃⶹॳᓣ↣ϔ乍ⱘߚ↡Ёབᵰ㸹ϞߚᄤЁⱘ᭄ˈህӮᰃ � Ͼ䖲㓁㞾✊᭄ⱘЬ⿃ˈ᠔ҹৃҹ ܜᇚ↣ϔ乍ⱘߚᄤǃߚ↡䛑ЬҹߚᄤЁⱘ᭄ˊे˖� ॳᓣ 2 2 2 23 4 5 12 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 10 11 12 13 14 � � � �u u u u u u u u u u u u u u u u" � ⦄೼䖯㸠㺖乍ⱘ䆱᮴⊩ܼ䚼Ⳍ⍜ 䳔ˈ㽕ᇍߚᄤ䖯㸠ߚᢚ 㗗ˈ㰥ࠄ↣ϔ乍Ёߚᄤǃߚ↡ⱘᇍ⿄ᗻˈ ৃҹ⫼ᑇᮍᏂ݀ᓣ˖ 23 1 5 4 u � ˈ 24 2 6 4 u � ˈ 25 3 7 4 u � ĂĂ� ࠓࠓ๥๥€€��ॳᓣ 2 2 2 23 4 5 12 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 10 11 12 13 14 � � � �u u u u u u u u u u u u u u u u" � 1 5 4 2 6 4 3 7 4 10 14 4 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 10 11 12 13 14 u � u � u � u � � � � �u u u u u u u u u u u u u u u u" � 1 1 1 1 2 3 4 3 4 5 4 5 6 11 12 13 4 4 4 4 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 10 11 12 13 14 § · � � � �¨ ¸u u u u u u u u© ¹ § ·� � � � �¨ ¸u u u u u u u u u u u u u u u u© ¹ " " � 1 1 1 1 1 1 1 2 2 3 3 4 3 4 4 5 11 12 12 13 1 1 1 1 1 1 1 2 3 4 2 3 4 5 2 3 4 5 3 4 5 6 10 11 12 13 11 12 13 14 § · u � � � � � �¨ ¸u u u u u u© ¹ § ·� � � � � � �¨ ¸u u u u u u u u u u u u u u u u u u© ¹ " " � 1 1 1 1 1 2 2 3 12 13 1 2 3 4 11 12 13 14 § · § · u � � �¨ ¸ ¨ ¸u u u u u u u u© ¹ © ¹ � 1 1 1 1 12 2 12 13 24 11 12 13 14 � � �u u u u u 1 77 1 8 11 12 13 14 � � u u u 1 1 8 2 11 14 � u u 1 1 75 8 308 616 � � ǏǏ՟ 3ǐ� 1 2 3 4 9 2 2 3 2 3 4 2 3 4 5 2 3 4 10 � � � � �u u u u u u u u u" " � ࠓࠓ๥๥€€��ॳᓣ 1 2 3 4 9 2 2 3 2 3 4 2 3 4 5 2 3 4 10 � � � � �u u u u u u u u u" " � 2 1 3 1 4 1 10 1 2 2 3 2 3 4 2 3 4 10 � � � � � � � �u u u u u u" " � 1 1 1 1 1 1 11 2 2 2 3 2 3 2 3 4 2 3 4 9 2 3 4 9 10 � � � � � � � �u u u u u u u u u u u" " " � 1 36287991 2 3 4 9 10 3628800 � u u u u" � Ǐ՟ 4ǐ� 1 1 1 1 1 1 2 1 2 3 1 2 100 � � � �� � � � � �"" " ��� ࠓࠓ๥๥€€��ᴀ乬Ў݌ൟⱘĀ䱤㮣೼ㄝᏂ᭄߫∖੠݀ᓣ㚠ৢⱘߚ᭄㺖Ꮒൟ㺖乍ā䯂乬DŽℸ㉏䯂乬䳔㽕Ң᳔ㅔ ऩⱘ乍ᓔྟܹ᠟ˈ䗮䖛݀ᓣⱘ䖤ㅫᇏᡒ㾘ᕟDŽҢ㄀ϔ乍ᓔྟˈᇍߚ↡䖯㸠ㄝᏂ᭄߫∖੠䖤ㅫ݀ ᓣⱘҷܹ᳝ 1 1 2(1 1) 11 1 2 2 � u u ˈ 1 1 2 (1 2) 21 2 2 3 2 � u� u ˈĂĂˈ�� ॳᓣ 2 2 2 2 1 200 992 (1 ) 1 1 2 2 3 3 4 100 101 101 101 101 � � � � u � u u u u"" � ٧٧څڅ€€�� 2 3 4 50 1 (1 2) (1 2) (1 2 3) (1 2 3) (1 2 3 4) (1 2 3 49) (1 2 3 50) � � � �u � � u � � � � u � � � � � � � u � � � �" " " ॳᓣ˙ 2 1 3u ˇ 3 3 6u ˇ 4 6 10u ˇ 5 10 15u ˇĂˇ 50 1225 1275u � ˙˄ 1 1 � 1 3 ˅ˇ˄ 1 3 � 1 6 ˅ˇ˄ 1 6 � 1 10 ˅ˇ˄ 1 1225 � 1 1275 ˅˙1274 1275 � ٧٧څڅ€€�� 2 3 4 100 1 (1 2) (1 2) (1 2 3) (1 2 3) (1 2 3 4) (1 2 99) (1 2 100) � � � �u � � u � � � � u � � � � � � u � � �" " " � ࠓࠓ๥๥€€�� 2 1 1 1 (1 2) 1 1 2 �u � � ˈ 3 1 1 (1 2) (1 2 3) 1 2 1 2 3 �� u � � � � � ˈĂĂˈ� 100 1 1 (1 2 99) (1 2 100) 1 2 99 1 2 100 �� � � u � � � � � � � � �" " " " ˈ᠔ҹ� ॳᓣ 11 1 2 100 � � � �" 1 50491 5050 5050 � � ٧٧څڅ€€�� 2 3 101 1 1 2 (1 2) (1 2 3) (1 2 3 9) (1 2 3 10)� � � �u � � u � � � � � � u � � � �" " "˄ ˅ � ࠓࠓ๥๥€€��ॳᓣ 2 3 4 101 ( ) 1 3 3 6 6 10 45 55 � � � � �u u u u" � 1 1 1 1 1 1 11 1 3 3 6 6 10 45 55 § · � � � � � � � � �¨ ¸© ¹" � 11 1 55 § · � �¨ ¸© ¹ 1 55 � ǏǏ՟ 5ǐ� 2 2 2 2 2 2 1 1 1 1 1 1 3 1 5 1 7 1 9 1 11 1 13 1 � � � � � � � � � � � ����������� ࠓࠓ๥๥€€��䖭乬ᰃ߽⫼ᑇᮍᏂ݀ᓣ䖯㸠㺖乍˖ 2 2 ( ) ( )a b a b a b� � u � ˈ� ॳᓣ 1 1 1 1 1 1( ) ( ) ( ) ( ) ( ) ( ) 2 4 4 6 6 8 8 10 10 12 12 14 � � � � �u u u u u u � 1 1 1 1 1 1 1 1 1 1 1 1 1( ) 2 4 4 6 6 8 8 10 10 12 12 14 2 � � � � � � � � � � � u � 1 1 1 3( ) 2 14 2 14 � u � ٧٧څڅ€€��䅵ㅫ˖ 2 2 2 2 2 2 2 2 3 5 7 15 1 2 2 3 3 4 7 8 � � � �u u u u" � ࠓࠓ๥๥€€��ॳᓣ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 3 2 4 3 8 7 1 2 2 3 3 4 7 8 � � � � � � � �u u u u" � 2 2 2 2 2 2 2 1 1 1 1 1 1 11 2 2 3 3 4 7 8 � � � � � � � �" 211 8 � 63 64 � ٧٧څڅ€€��䅵ㅫ˖ 2 2 2 2 2 2 2 2 2 2 3 1 5 1 7 1 1993 1 1995 1 3 1 5 1 7 1 1993 1 1995 1 � � � � �� � � � � � � � � �" ����������ˊ� ࠓࠓ๥๥€€��ॳᓣ 2 2 2 2 2 2 2 2 2 21 1 1 1 1 3 1 5 1 7 1 1993 1 1995 1 § · § · § · § · § · � � � � � � � � � �¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸� � � � �© ¹ © ¹ © ¹ © ¹ © ¹" � 2 2 2997 2 4 4 6 1994 1996 § · � � � �¨ ¸u u u© ¹" � 1 1 1 1 1 1997 2 4 4 6 1994 1996 § · � � � � � � �¨ ¸© ¹" 1 1997 2 1996 § · � �¨ ¸© ¹ 997997 1996 � ٧٧څڅ€€��䅵ㅫ˖ 2 2 2 21 2 3 50 1 3 3 5 5 7 99 101 � � � � u u u u" ����������ˊ� ࠓࠓ๥๥€€��ᓣᄤЁ↣ϔ乍ⱘߚᄤϢߚ↡߱ⳟ䍋ᴹ݇㋏ϡ໻ˈԚᰃབᵰᇚ݊Ёⱘߚ↡ḍ᥂ᑇᮍᏂ݀ᓣߚ߿ব Ў 22 1� ˈ 24 1� ˈ 26 1� ˈĂĂˈ 2100 1� ˈৃҹথ⦄བᵰߚ↡䛑ࡴϞ �ˈ䙷Мᙄད䛑ᰃߚᄤ ⱘ �סˈ᠔ҹৃҹܜᇚॳᓣЬҹ �ৢ䖯㸠䅵ㅫˈᕫߎ㒧ᵰৢ䰸ҹ �ህᕫࠄॳᓣⱘؐњˊ� ॳᓣ 2 2 2 2 2 2 2 2 1 2 4 6 100 4 2 1 4 1 6 1 100 1 § · u � � � �¨ ¸� � � �© ¹ " � 2 2 2 2 1 1 1 1 11 1 1 1 4 2 1 4 1 6 1 100 1 § · u � � � � � � � �¨ ¸� � � �© ¹" � 1 1 1 1 150 4 1 3 3 5 5 7 99 101 § · u � � � � �¨ ¸u u u u© ¹" � 1 1 1 1 1 1 1 1 150 1 4 2 3 3 5 5 7 99 101 ª º§ · u � u � � � � � � � �¨ ¸« »© ¹¬ ¼" � 1 1 150 1 4 2 101 ª º§ · u � u �¨ ¸« »© ¹¬ ¼ 1 5050 4 101 u 6312 101 � ٧٧څڅ€€��2 2 4 4 6 6 8 8 10 10 1 3 3 5 5 7 7 9 9 11 u u u u u� � � �u u u u u ����� ࠓࠓ๥๥€€��˄ ⊩ �˅˖ ৃܜᡒ䗮乍 2 2 2 1 11 1 1 1 ( 1) ( 1)n na n n n n � �� � � u � � ॳᓣ 1 1 1 1 1(1 ) (1 ) (1 ) (1 ) (1 ) 1 3 3 5 5 7 7 9 9 11 � � � � � � � � �u u u u u � 1 1 5 55 (1 ) 5 5 2 11 11 11 � u � � � ˄⊩ �˅˖ ॳᓣ 2 8 8 18 18 32 32 50 50(2 ) ( ) ( ) ( ) ( ) 3 3 5 5 7 7 9 9 11 � � � � � � � � � � 6 10 14 18 50 6 52 10 4 5 3 5 7 9 11 11 11 � � � � � � � ǏǏ՟ 6ǐ� 1 11 3 19992 1 1 1 1 1 11 (1 ) (1 ) (1 ) (1 ) (1 ) 2 2 3 2 3 1999 � � � � � u � � u � u u � " " ���� ࠓࠓ๥๥€€�� 1 1 2 1 11 1 2 ( ) 1 1 1 2 ( 1)( 2) 1 2(1 ) (1 ) (1 ) 2 3 1 2 n n n n n n n n � � u �� � � � �� u � u u � �" � ॳᓣ˙ 1 1 1 1 1 1 1 1( ) ( ) ( ) ( ) 2 2 3 3 4 4 5 1999 2000 ª º� � � � � � � � u« »¬ ¼" ˙ � ٧٧څڅ€€��䅵ㅫ˖ 1 1 11 1 2 1 2 3 1 2 2007 � � �}� � � � �} � ࠓࠓ๥๥€€��ܜᡒ䗮乍݀ᓣ 1 2 1 12( ) 1 2 ( 1) 1n a n n n n n �� � u � �" � ॳᓣ 1 1 11 2 (2 1) 3 (3 1) 2007 (2007 1) 2 2 2 � � � �u � u � u �" � 2 2 2 2 1 2 2 3 3 4 2007 2008 � � � �u u u u" � 20072 2008 u � 2007 1004 � ٧٧څڅ€€��1 1 1 1 3 3 5 3 5 7 3 5 7 21 � � � �� � � � � � �" " � ࠓࠓ๥๥€€��ܜᡒ䗮乍˖ � � � � � � 1 1 1 13 5 2 1 22 1 3 2 na n n nn n � � � � �u � � u" ˈ� ॳᓣ 1 1 1 1 1 1 1 3 2 4 3 5 4 6 9 11 10 12 � � � � � �u u u u u u" � 1 1 1 1 1 1 1 3 3 5 9 11 2 4 4 6 10 12 § · § · � � � � � � �¨ ¸ ¨ ¸u u u u u u© ¹ © ¹" " � 1 1 1 1 1 1 2 1 11 2 2 12 § · § · u � � u �¨ ¸ ¨ ¸© ¹ © ¹ � 175 264 � Ǐ՟ 7ǐ� 1 2 1 2 3 1 2 3 4 1 2 3 50 2 2 3 2 3 4 2 3 50 � � � � � � � � � �u u u u� � � � � � "" " ��� ࠓࠓ๥๥€€��ᡒ䗮乍 (1 ) ( 1)2 (1 ) ( 1) 21 2 n n n n na n n n n � u u � � u u � �� � ॳᓣ 2 3 3 4 4 5 5 6 2 3 3 4 4 5 5 6 4 10 18 28 1 4 2 5 3 6 4 7 u u u u u u u u u u u u u u u uu u u u" "ˈ� 䗮䖛䆩ݭ៥Ӏজথ⦄᭄߫ᄬ೼ҹϞ㾘ᕟˈ䖭ḋ៥Ӏህৃҹ䕏ᵒݭߎܼ䚼ⱘ乍ˈ᠔ҹ᳝� ॳᓣ 2 3 3 4 4 5 5 6 48 49 49 50 50 51 1 4 2 5 3 6 4 7 47 50 48 51 49 52 u u u u u u u u u u u u u uu u u u u u u" 3 50 232 1 52 26 u � � � � � 1000 999 1000 11 � ǏǏ՟ 8ǐ� 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 2 1 2 3 1 2 3 4 1 2 26 1 1 2 1 2 3 1 2 3 4 1 2 26 � � � � � � � �}�� � � �}�� � � � � � � �}� � ࠓࠓ๥๥€€�� 2 2 2 2 23 3 3 ( 1) (2 1) 1 2 2 2 1 2 1 16 ( ) ( 1)1 2 3 ( 1) 3 1 4 n n n n n na n nn n n n n u � u � � �}� � u u �u �� �}� u � � � ॳᓣ 2 1 1 1 1 1 1 1 1[( ) ( ) ( ) ( )] 3 1 2 2 3 3 4 26 27 u � � � � � � �"" 2 1 52(1 ) 3 27 81 u � � ٧٧څڅ€€�� 2 2 2 1 1 11 1 1 2 1 3 1 99 1 § · § · § ·� u � u u �¨ ¸ ¨ ¸ ¨ ¸� � �© ¹ © ¹ © ¹" � ࠓࠓ๥๥€€�� 2 2 2 2 1 ( 1) ( 1)1 ( 1) 1 ( 1) 1 ( 2)n n na n n n n � � � � � � � u � � ॳᓣ 2 2 3 3 98 98 99 99 (2 1) (2 1) (3 1) (3 1) (98 1) (98 1) (99 1) (99 1) u u u u u u u u� u � � u � � u � � u �" � 2 2 3 3 4 4 5 5 98 98 99 99 2 99 491 3 1 4 2 5 3 6 4 99 97 100 98 1 100 50 u u u u u u u u u u u u u u u u u u u" � Ǐ՟ 9ǐ�䅵ㅫ˖ 2 2 2 2 2 2 2 3 99 2 1 3 1 99 1 u u u � � �" � ࠓࠓ๥๥€€��䗮乍݀ᓣ˖ � �� �� � � � � � 2 21 1 1 1 1 1 2n n n a n n n n � � � � � � � ˈॳᓣ 2 2 3 3 4 4 98 98 99 99 (2 1) (2 1) (3 1) (3 1) (4 1) (4 1) (98 1) (98 1) (99 1) (99 1) u u u u u u u u u u� u � � u � � u � � u � � u �" � 2 2 3 3 4 4 5 5 98 98 99 99 3 1 4 2 5 3 6 4 99 97 100 98 u u u u u u u u u u u uu u u u u u" � 2 2 3 3 4 4 98 98 99 99 1 3 2 4 3 5 97 99 98 100 u u u u u u u u u u" 2 99 99 1 100 50 u � ٧٧څڅ€€��䅵ㅫ˖ 2 2 2 2 2 2 1 2 99 1 100 5000 2 200 5000 99 9900 5000 � � � � � � � � �" ����������� ࠓࠓ๥๥€€��ᴀ乬ⱘ䗮乍݀ᓣЎ 2 2 100 5000 n n n� � ˈ≵ࡲ⊩䖯㸠㺖乍П㉏ⱘ໘⧚ˊ⊼ᛣࠄߚ↡ � � � � � �2 100 5000 5000 100 5000 100 100 100n n n n n n� � � � � � � �ª º¬ ¼ ˈৃ ҹⳟߎབᵰ ᡞ nᤶ៤100 n� ⱘ䆱ߚ↡ⱘؐϡব ᠔ˈҹৃҹᡞॳᓣᄤЁⱘߚ᭄ϸϸ㒘ড়䍋ᴹˈ᳔ ৢऩ⣀࠽ϟ ϔϾ 2 2 50 50 5000 5000� � ˊᇚ乍᭄੠Ў ���ⱘϸ乍Ⳍࡴˈᕫ� � � � � � � � �2 222 2 22 2 2 100 100 2 200 10000 2 100 5000 100 5000 100 5000100 100 100 5000 n n nn n n n n n n n nn n � � � � �� � � � � � �� � � � � ᠔ҹॳᓣ 2 49 1 99 u � ˊ˄ ៪㗙ˈৃᕫॳᓣЁ ��乍ⱘᑇഛ᭄Ў �ˈ᠔ҹॳᓣ 1 99 99 u �˅ Ǐ՟���ǐ� ¹¸ · ©¨ § ��������¹¸ · ©¨ § u��u�uu 222222 1021 1 21 1 1 1 2120 1 54 1 32 124 """ � � ࠓࠓ๥๥€€��㱑✊ᕜᆍᯧⳟߎ 32 1 u ˙ 3 1 2 1 � ˈ 54 1 u ˙ 5 1 4 1 � ĂĂৃᰃݡҨ㒚ϔⳟ ᑊˈ≵᳝ҔМᬜᵰ ಴ˈЎ 䖭ϡ䈵ߚ᭄㺖乍䙷ḋ㛑⍜এᕜ໮乍ˊ៥Ӏݡᴹⳟৢ䴶ⱘᓣᄤˈ↣ϔ乍ⱘߚ↡ᆍᯧ䅽៥Ӏᛇࠄ݀ ᓣ�ˈѢᰃ៥Ӏজ᳝ )12()1( 6 321 1 2222 �u�u���� nnnn ˙" ˊˊ ޣোࠡ䴶ᣀো䞠ⱘᓣ ᄤ᳝ ��乍ˈޣোৢ䴶ᣀো䞠ⱘᓣᄤгᙄད᳝ ��乍ˈᰃϡᰃĀϔϾᇍϔϾāਸ਼˛� �� � ¹¸ · ©¨ § ��������¹¸ · ©¨ § u��u�uu 222222 1021 1 21 1 1 1 2120 1 54 1 32 124 """ � ˙ ¹¸ · ©¨ § uu��uu�uuu�¹¸ · ©¨ § u��u�uu 211110 1 532 1 321 16 2120 1 54 1 32 124 "" � ˙ ¹¸ · ©¨ § uu��uu�uuu�¹¸ · ©¨ § u��u�uu 212220 1 564 1 342 124 2120 1 54 1 32 124 "" � ˙ »¼ º«¬ ª ¹¸ · ©¨ § uu�u��¹¸ · ©¨ § uu�u�¹¸ · ©¨ § uu�uu 212220 1 2120 1 564 1 54 1 342 1 32 124 " � ˙ ¹¸ · ©¨ § u��u�uu 2220 1 64 1 42 124 " ˙ ¹¸ · ©¨ § u��u�uu 1110 1 32 1 21 16 " ˙ ¹¸ · ©¨ § �u 11 116 ˙ 11 60 ˊ � ῵ഫѠǃᤶܗϢ݀ᓣᑨ⫼� ǏǏ՟ 11ǐ�䅵ㅫ˖ 3 3 3 3 3 3 3 31 3 5 7 9 11 13 15� � � � � � � � ࠓ๥€�ॳᓣ � �3 3 3 3 3 3 3 3 31 2 3 4 14 15 2 4 14 � � � � � � � � � �" " � � � � �22 3 3 315 15 1 8 1 2 7 4 u � � u � � �" 2 257600 2 7 8 4 � u u 8128 � � ٧٧څڅ€€��1 3 2 4 3 5 9 11u � u � u � u" � ࠓ๥€�ॳᓣ � �� � � �� � � �� �2 1 2 1 3 1 3 1 10 1 10 1 � � � � � � � � �" � � � � � � � � � � 2 2 2 2 2 2 2 2 2 2 2 1 3 1 10 1 2 3 10 9 10 11 211 2 3 10 10 10 375 6 � � � � � � � � � � u u � � � � � � " " " � ٧٧څڅ€€��䅵ㅫ˖1 2 3 2 3 4 3 4 5 8 9 10u u � u u � u u � � u u" � ࠓ๥€�ॳᓣ � � � � � � � �2 2 2 22 2 1 3 3 1 4 4 1 9 9 1 u � � u � � u � � � u �" � � �3 3 3 32 3 4 9 2 3 4 9 � � � � � � � � �" " � � � � �21 2 3 9 1 2 3 4 9 � � � � � � � � � �" " 245 45 1980 � � Ǐ՟ 12ǐ�䅵ㅫ˖ 2 3 4 5 6 1 1 1 1 1 11 3 3 3 3 3 3 � � � � � � �� ࠓ๥€�⊩ϔ˖߽⫼ㄝ↨᭄߫∖੠݀ᓣDŽ� ॳᓣ 711 1 3 11 3 ª º§ ·u �« »¨ ¸© ¹« »¬ ¼ � 71 3 2641 1 3 2 729 ª º§ · � u « »¨ ¸© ¹« »¬ ¼ � ⊩Ѡ˖䫭ԡⳌޣ⊩ˊ� 䆒 2 3 4 5 6 1 1 1 1 1 11 3 3 3 3 3 3 S � � � � � � � ߭ 2 3 4 5 1 1 1 1 13 3 1 3 3 3 3 3 S � � � � � � ˈ 613 3 3S S� � ˈᭈ⧚ৃᕫ 3641 729 S ˊ� ⊩ϝ˖ᴀ乬Ϣ՟ � Ⳍ↨ˈᓣᄤЁ৘乍䛑ᰃ៤ㄝ↨᭄߫ˈԚᰃ՟ � ЁⱘߚᄤЎ �ˈϢ݀↨ � Ꮒ �ˈ � ᠔ҹৃҹ䞛⫼Ā׳ᴹ䖬এāⱘᮍ⊩ˈᴀ乬བᵰг㽕䞛⫼Ā׳ᴹ䖬এāⱘᮍ⊩ˈ䳔㽕ᇚ↣ϔ乍ⱘ ߚᄤবᕫг䛑Ϣ݀↨Ꮒ �ˊ⬅Ѣ݀↨Ў �ˈ㽕ᡞߚᄤবЎ �ˈৃҹܜᇚ↣ϔ乍䛑Ьҹ �䖯㸠ㅫˈ᳔ৢ ݡᇚ᠔ᕫⱘ㒧ᵰ䰸ҹ �ेᕫࠄॳᓣⱘؐˊ⬅乬䆒ˈ 2 3 4 5 6 2 2 2 2 2 22 2 3 3 3 3 3 3 S � � � � � � ˈ߭䖤⫼ Ā׳ᴹ䖬এāⱘᮍ⊩ৃᕫࠄ 6 12 3 3 S � ˈᭈ⧚ᕫࠄ 3641 729 S ˊ� � ǏǏ՟ 13ǐ�䅵ㅫ˖ 2 2 2 2 2 2 2 2(2 4 6 100 ) (1 3 5 99 ) 1 2 3 9 10 9 8 3 2 1 � � � ˜ ˜ ˜ � � � � � ˜ ˜ ˜ � � � � ˜ ˜ ˜ � � � � � ˜ ˜ ˜ � � � � ࠓ๥€�ॳᓣ 2 2 2 2 2 2 2 2 2 (2 1 ) (4 3 ) (6 5 ) (100 99 ) 10 � � � � � � ˜ ˜ ˜ � � � (2 1) (2 1) (4 3) (4 3) (6 5) (6 5) (100 99) (100 99) 100 � u � � � u � � � u � � ˜˜ ˜ � � u � � 1 2 3 4 99 100 5050 150 100 100 2 � � � � ˜˜ ˜ � � � ٧٧څڅ€€��Ł � �231415926 31415925 31415927� u BBBBBBBB˗� ���������ł 2 21234 8766 2468 8766� � u BBBBBBBBˊ� ࠓ๥€�Ł� 㾖ᆳৃⶹ ��������੠ ��������䛑Ϣ ��������ⳌᏂ �ˈ䆒 31415926a ˈ� ॳᓣ � �� � � �2 2 21 1 1 1a a a a a � � � � � � ł� ॳᓣ 2 21234 8766 2 1234 8766 � � u u � �2 21234 8766 10000 100000000 � � ٧٧څڅ€€��䅵ㅫ˖ 2 2 2 2 2 2 21 2 3 4 2005 2006 2007� � � � � � �" � ࠓ๥€�ॳᓣ 2 2 2 2 2 2 22007 2006 5 4 3 2 1 � � � � � � �" � � (2007 2006) (2007 2006) (2005 2004) (2005 2004) (3 2) (3 2) 1 � u � � � u � � � � u � �" � ������������� 2007 2006 2005 2004 3 2 1 � � � � � � �" � ������������� � �1 2007 1 2007 2015028 2 u � u � Ǐ՟ 14ǐ�䅵ㅫ˖ 2 2 2 2 2 2 2 2 2 21 2 2 3 3 4 4 5 2000 2001 1 2 2 3 3 4 4 5 2000 2001 � � � � �� � � � ˜ ˜ ˜ �u u u u u � ࠓ๥€�ॳᓣ 2 2 2 2 2 2 2 2 2 21 2 2 3 3 4 4 5 2000 2001 1 2 1 2 2 3 2 3 3 4 3 4 4 5 4 5 2000 2001 2000 2001 � � � � � � � � ˜ ˜ ˜ � �u u u u u u u u u u � 1 2 2 3 3 4 4 5 2000 2001 2 1 3 2 4 3 5 4 2001 2000 � � � � � � � � ˜˜ ˜ � � � � �������� � ����������������������������� 2 1 3 2 4 3 5 1999 2001 2000( ) ( ) 1 2 2 3 3 4 4 2000 2000 2001 § · § · � � � � � � � ˜ ˜ ˜ � � �¨ ¸ ¨ ¸© ¹ © ¹ � 2000 2000 20002 2 2 2 2 4000 2001 2001 � � � � ˜ ˜ ˜ � � ���� ��� Ͼ�Ⳍࡴ � Ǐ՟ 15ǐ� � �2007 8.5 8.5 1.5 1.5 10 160 0.3� u � u y y � ª º¬ ¼ ���������ˊ� ࠓ๥€�ॳᓣ � �� �2007 8.5 1.5 8.5 1.5 10 160 0.3 � � � y y �ª º¬ ¼ � �2007 10 8.5 1.5 10 160 0.3 � u � y y �ª º¬ ¼ � �2007 7 160 0.3 � y � 12.5 0.3 � 12.2 � ٧٧څڅ€€��䅵ㅫ˖ 53 57 47 43u � u ���������ˊ� ࠓ๥€�ᴀ乬ৃҹⳈ᥹ᇚϸϾЬ⿃䅵ㅫߎᴹݡ∖ᅗӀⱘᏂˈԚ♉⌏䞛⫼ᑇᮍᏂ݀ᓣ㛑ᬊࠄ᳈དⱘᬜᵰˊ� � ॳᓣ � � � � � � � �55 2 55 2 45 2 45 2 � u � � � u � � �2 2 2 255 2 45 2 � � � � � � � � �2 255 45 55 45 55 45 1000 � � u � � ٧٧څڅ€€��䅵ㅫ˖11 19 12 18 13 17 14 16u � u � u � u ���������ˊ� ࠓ๥€�ᴀ乬ৃҹⳈ᥹䅵ㅫߎ৘乍Ь⿃ݡ∖੠ˈгৃҹ䞛⫼ᑇᮍᏂ݀ᓣˊ� � ॳᓣ � � � � � � � �2 2 2 2 2 2 2 215 4 15 3 15 2 15 1 � � � � � � � � � � �2 2 2 2 215 4 1 2 3 4 u � � � � 900 30 870 � � ��������݊Ё 2 2 2 21 2 3 4� � � ৃҹⳈ᥹䅵ㅫˈԚབᵰ乍᭄䕗໮ˈᑨ䞛⫼݀ᓣ� � � �� �2 2 2 11 2 1 2 1 6 n n n n� � � � �" 䖯㸠䅵ㅫˊ� ٧٧څڅ€€��䅵ㅫ˖1 99 2 98 3 97 49 51u � u � u � � u " ����������ˊ� ࠓ๥€�㾖ᆳথ⦄ᓣᄤЁ↣ⳌЬⱘϸϾ᭄ⱘ੠䛑ᰃⳌㄝⱘˈৃҹ䞛⫼ᑇᮍᏂ݀ᓣˊ� � ॳᓣ � � � � � � � � � � � �50 49 50 49 50 48 50 48 50 1 50 1 � u � � � u � � � � u �" � � � � � � � �2 2 2 2 2 250 49 50 48 50 1 � � � � � �" � � � �2 2 2 250 49 1 2 49 u � � � �" � � � �2 2 2 250 49 1 2 49 u � � � �" � � 2 150 49 49 50 99 6 u � u u u � � 250 49 49 25 33 u � u u � � � �49 25 100 33 u u � � � 49 25 67 u u � � 82075 � ٧٧څڅ€€��ⳟ㾘ᕟ� 3 21 1 ˈ 3 3 21 2 3� ˈ 3 3 3 21 2 3 6� � ĂĂˈ䆩∖ 3 3. 36 7 14� � �" � � ॳᓣ � � � �3 3. 3 3 3. 31 2 14 1 2 5 � � � � � � �" " � � � �2 21 2 3 14 1 2 3 4 5 � � � � � � � � �" � �� �2 2105 15 105 15 105 15 � � � 90 120 10800 u � Ǐ՟ 16ǐ�䅵ㅫ˖ 1 1 1 1 1 1 1 1 1 1(1 ) ( ) (1 ) ( ) 2 4 2 4 6 2 4 6 2 4 � � u � � � � � � u � �� ࠓ๥€�Ҹ 1 1 11 2 4 6 a� � � ˈ 1 1 1 2 4 6 b� � ˈ߭˖� � ॳᓣ 1 1( ) ( ) 6 6 a b a b � u � u � 1 1 6 6 ab b ab a � � � 1 ( ) 6 a b � 1 11 6 6 u � ٧٧څڅ€€�� 1 1 1 1 1 1 1 1 1 1 1 1 1 1(1 ) ( ) (1 ) ( ) 2 3 4 2 3 4 5 2 3 4 5 2 3 4 � � � u � � � � � � � � u � � � ࠓ๥€�䆒 1 1 1 2 3 4 a � � ˈ߭ॳᓣ࣪ㅔЎ˖ 1 1 11 (1 5 5 5 a a a a�� � �� � �� � � � ٧٧څڅ€€�� 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 21 31 41 21 31 41 51 11 21 31 41 51 21 31 41 § · § · § · § ·� � � u � � � � � � � � u � �¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸© ¹ © ¹ © ¹ © ¹ ��������� ࠓ๥€�䆒 1 1 1 1 11 21 31 41 a� � � ˈ 1 1 1 21 31 41 b� � ˈ� � ॳᓣ 1 1 51 51 a b a b§ · § · u � � � u¨ ¸ ¨ ¸© ¹ © ¹ 1 1 51 51 ab a ab b � � � 1 ( ) 51 a b � � 1 1 1 51 11 561 u � ٧٧څڅ€€��� 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1( ) ) ( ) 5 7 9 11 7 9 11 13 5 7 9 11 13 7 9 11 � � � u � � � � � � � � u � �˄ ˅ ˄ ���� ࠓ๥€�䆒 1 1 1 1 5 7 9 11 A� � � ˈ 1 1 1 7 9 11 B� � ˈ� � ॳᓣ 1 1 13 13 A B A B§ · § · u � � � u¨ ¸ ¨ ¸© ¹ © ¹ 1 1 13 13 A B A A B B u � � u � � �1 13 A B � � 1 1 1 13 5 65 u � ٧٧څڅ€€��䅵ㅫ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 2 3 4 5 2 3 4 5 6 2 3 4 5 6 2 3 4 5 § · § · § · § ·� � � � u � � � � � � � � � � u � � �¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸© ¹ © ¹ © ¹ © ¹ � ࠓ๥€�䆒 1 1 1 11 2 3 4 5 A� � � � ˈ 1 1 1 1 2 3 4 5 B� � � ˈ � ॳᓣ � 1 1 6 6 A B A B§ · § ·u � � � u¨ ¸ ¨ ¸© ¹ © ¹ 1 1 6 6 A B A A B Bu � u � u � u 1 1 6 6 A Bu � u 1 6 u � A B� � 1 6 � ٧٧څڅ€€��� 21 2 3 9 1 2 3 9 1 1 2 9 2 3 91 2 3 4 10 2 3 4 10 2 2 3 10 3 4 10 § · § · § · § ·� � � � �
本文档为【分数的速算与巧算】,请使用软件OFFICE或WPS软件打开。作品中的文字与图均可以修改和编辑, 图片更改请在作品中右键图片并更换,文字修改请直接点击文字进行修改,也可以新增和删除文档中的内容。
该文档来自用户分享,如有侵权行为请发邮件ishare@vip.sina.com联系网站客服,我们会及时删除。
[版权声明] 本站所有资料为用户分享产生,若发现您的权利被侵害,请联系客服邮件isharekefu@iask.cn,我们尽快处理。
本作品所展示的图片、画像、字体、音乐的版权可能需版权方额外授权,请谨慎使用。
网站提供的党政主题相关内容(国旗、国徽、党徽..)目的在于配合国家政策宣传,仅限个人学习分享使用,禁止用于任何广告和商用目的。
下载需要: 免费 已有0 人下载
最新资料
资料动态
专题动态
is_495769
暂无简介~
格式:pdf
大小:240KB
软件:PDF阅读器
页数:17
分类:初中数学
上传时间:2013-01-22
浏览量:206