2003亞洲城市青少年數學邀請賽
初中組隊際賽 2003.8.7 中國福州一中
Asia Inter-cities Teenagers Mathematics Invitation Competition
Middle School Team Contest 2003.8.7
Fuzhou No.1 Middle School of China
隊名(Team)：　　　　　 　　
4/5+44/45+116/117+.............+1220/1221 求的值。
請問答案是8+28/37嗎
順便問一下要怎麼把數學式子貼上去ㄋ

我幫你貼吧....

原式

= (1-1/5)+(1-1/45)+(1-1/117)+...+(1-1/1221)

= (1+1+...+1) - [1/(1*5)+1/(5*9)+1/(9*13)+...+1/(33*37)]

(由等差數列得知共有 9 項)

= 9-(1/4)[1-(1/5)+(1/5)-(1/9)+(1/9)-(1/13)+...+(1/33)-(1/37)]

(準備用分項對消法了)

= 9 - (1/4)[1-(1/37)]

= 9 - (1/4)(36/37)

= 9 - (9/37)

= 8 又 28/37

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孩子們, 別再問我為何每天都穿 KAPPA 了!

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