Represent the function f(x) = x/(1+4x)^2 as a power series and determine the radius of convergence.

so the correct answer is (-1)^n * (n+1) *4^n*x^(n+1) but this is what I got:

x/(1+4x)^2

x/[1-(-4x)^2

x series sign (-4x)^n

series sign (-1)^n * 4^n x^(n+1)

Where did the (n+1) in front of the 4^n come from?