Find the values of x for which the series ∞Σ(n=1) (3^n)/(x^n) converges. Find the sum for those values of x.?

2016-03-28 5:23 am

回答 (1)

2016-03-28 8:07 am
✔ 最佳答案
1.
(1)
a_n = 3^n / x^n = (3/x)^n
a_n+1 / a_n = (3/x)^(n+1) / (3/x)^n = 3/x
|3/x|< 1 即收斂
故 |x|> 3
x > 3 or x < - 3 ..... Ans

(2)
此級數為等比級數, 公比 = 3/x
S
= (3/x) / [ 1 - 3/x ]
= (3/x) / [ ( x - 3 )/x ]
= 3 / ( x - 3 ) ..... Ans


收錄日期: 2021-04-29 12:04:08
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160327212359AAB0y59

檢視 Wayback Machine 備份