數列求Sn通項公式 - Ans.fyi 參考答案

數列求Sn通項公式

[匿名]

2010-10-13 4:58 am

S1=3,S2=7,S3=13,S4=23,S5=41....求Sn...
諗左好耐都諗唔到....希望有人幫到我=[

回答 (2)

用戶2053

2010-10-13 10:06 pm

✔ 最佳答案

S1 = 3 = (2 + 2^0)S2 = 7 = (2 + 2^0) + (2 + 2^1)S3 = 13 = (2 + 2^0) + (2 + 2^1) + (2 + 2^2)S4 = 23 = (2 + 2^0) + (2 + 2^1) + (2 + 2^2) + (2 + 2^3) S5 = 41 = (2 + 2^0) + (2 + 2^1) + (2 + 2^2) + (2 + 2^3) + (2 + 2^4)..........................................................................................................S(n) = (2 + 2^0) + (2 + 2^1) + (2 + 2^2) + (2 + 2^3) + ... + (2 + 2^(n-1))S(n) = (2 + 2 + 2 + 2 + ... + 2) + (2^0 + 2^1 + 2^2 + 2^3 + ... + 2^(n-1))S(n) = 2n + (2^0 + 2^1 + 2^2 + 2^3 + ... + 2^(n-1))S(n) = 2n + (2^0)(1 - 2^n) / (1 - 2)S(n) = 2n + (2^n - 1)

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doraemonpaul

2010-10-13 3:35 pm

3,7,13,23,41,......
4,6,10,18,......
2,4,8,......

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