# Math Help - Ratio Test, Convergence

1. ## Ratio Test, Convergence

Determine if $\sum_{j=0}^{\infty}\frac{j^2}{4^j}$ converges, using ratio test.

Ok so i know that it is $\lim_{j\to\infty}\mid\frac{\frac{(j+1)^2}{4^{j+1}} }{\frac{j^2}{4^j}}\mid$

Which comes to $\lim_{j\to\infty}\mid\frac{(j+1)^2}{4j^2}\mid$

Does that then become $\lim_{j\to\infty}\mid\frac{1}{4}\mid$ + $\lim_{j\to\infty}\mid\frac{2}{4j}\mid$ + $\lim_{j\to\infty}\mid\frac{1}{4j^2}\mid$ = 1/4

Therefore series converges as L<1?

2. ## Re: Ratio Test, Convergence

The solution of the limit is correct. The serie converges because $\frac{1}{4}<1$.