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.
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 (with partial sums .... )