The Problem:

summation as 'n' goes from 2 to infinity of n^20/2^n .

The ans says it converges to 1/2 but cant see how it does this since the terms seem to be increasing in magnitude when you plug numbers in.

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- Sep 9th 2010, 03:30 AMheatlyInfinite Series
The Problem:

summation as 'n' goes from 2 to infinity of n^20/2^n .

The ans says it converges to 1/2 but cant see how it does this since the terms seem to be increasing in magnitude when you plug numbers in. - Sep 9th 2010, 03:38 AMyeKciM

so you have that your a_n is

now apply some of the tests for convergence ...

you can use Cauchy's test of convergence :

or with D'Alambert's test for convergence :

or with Raabe's test of convergence :

or you can show by the definition that sum converges or diverges :D (with partial sums .... ) - Sep 9th 2010, 04:30 AMmr fantastic
- Sep 9th 2010, 04:52 AMyeKciM