# If I want to test the series #sum_(n=1)^oo(n^2+2^n)/(1-e^(n+1))# for convergence, what would be the best test to use and why?

##### 1 Answer

By pulling out the negative sign so that

I would use Limit Comparison Test since we can make a ball-park estimate of the series by only looking at the dominant terms on the numerator and the denominator. This series can be compared to

which is a convergent geometric series with

Let us make sure that they are comparable.

(Note:

So,

Hence,

I hope that this was helpful.