sum_(n=1)^oo (4x)^n/n^2 Find the radius of convergence of the power series.

sum_(n=1)^oo (4x)^n/n^2
To find radius of convergence of a series sum a_n , apply the Ratio Test. 
L = lim_(n->oo) |a_(n+1)/a_n|

L=lim_(n->oo) | (4x)^(n+1)/(n+1)^2 * n^2/(4x)^n|
L= lim_(n->oo) |(4xn^2)/(n+1)^2|
L = |4x| lim_(n->oo) |n^2/(n+1)^2|
L = |4x| * 1
L = |4x|
L =4|x|
Take note that in Ratio Test, the series converges when L < 1. 
L < 1
4|x| lt 1
|x|lt1/4
Therefore, the radius of convergence of the given series is R = 1/4 .