推 webber6418:謝謝你喔^^ 09/29 20:03
※ 引述《webber6418 (小超)》之銘言：
: 類題演練
: 試求:(1/10^1)+(2/10^2)+(3/10^3)+(4/10^4)+.....=?
: 答案:(10/81)
: 這題我已經想破頭還是找不出其規律性 麻煩大家惹
設 S = (1/10^1)+(2/10^2)+(3/10^3)+(4/10^4)+.....
(1/10)*S = (1/10^2)+(2/10^3)+(3/10^4)+(4/10^5)+....
兩是相減得
(9/10)*S = (1/10^1)+(1/10^2)+(1/10^3)+(1/10^4)+.....= 1/9
則 S = 10/81
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