What is the comparison function
Favorites|Homepage
Subscriptions | sitemap
HOME > > What is the comparison function

What is the comparison function

[From: ] [author: ] [Date: 12-11-01] [Hit: ]
we conclude that the series in question also converges.I hope this helps!......
I know the following function is convergent, but I'm not sure what the comparison function is.
FInd the comparison function of Summation from n=1 to infinity of (5+(-1)^n)/(n*n^(1/3))

I appreciate your help

-
Note that (5 + (-1)^n) / (n*n^(1/3)) always has positive terms since 5 + (-1)^n ≥ 5 - 1 = 4.
So, we can use the Comparison Test.

Next, (5 + (-1)^n) / (n*n^(1/3))
= (5 + (-1)^n) / n^(4/3)
≤ (5 + 1) / n^(4/3)
= 6/n^(4/3); this is your comparison function.

Since Σ(n = 1 to ∞) 6/n^(4/3) is convergent (being a multiple of a convergent p-series with p = 4/3 > 1), we conclude that the series in question also converges.

I hope this helps!
1
keywords: function,the,What,comparison,is,What is the comparison function
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .