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 _________________ 孩子們, 別再問我為何每天都穿 KAPPA 了!
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