How can I prove the summation of (n+1)/(n^(5/2)) converges using the Limit/Direct Comparison Test
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > How can I prove the summation of (n+1)/(n^(5/2)) converges using the Limit/Direct Comparison Test

How can I prove the summation of (n+1)/(n^(5/2)) converges using the Limit/Direct Comparison Test

[From: ] [author: ] [Date: 11-09-07] [Hit: ]
......
See the question.

-
By the limit comparison test if lim n-> infinity of a(n) / b(n) converges to nonzero real number then the series a(n) converges iff series b(n) converges
Here a(n) is (n+1)/n^(5/2)
Let b(n) = 1 / n^(3/2), then a(n)/ b(n) = [(n+1) / n^(5/2)][1 / n^(3/2)] = (n+1) / n
--> lim n-> infinity a(n) / b(n) = lim n-> infinity (n+1) n = 1
The ratio converges to a nonzero number and by the p-series test our series b(n) converges, hence by the limit comparison test our series converges
1
keywords: of,converges,Direct,How,using,Comparison,can,Test,prove,Limit,summation,the,How can I prove the summation of (n+1)/(n^(5/2)) converges using the Limit/Direct Comparison Test
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .