Find closed form of series SUM (nx)^(2n)

[Calculus!]

If abs x < 1 find a closed form function (i.e. f(x) = x +1) for the following series:

$$\sum((nx)^(2n))$$

(reads: the series from n=1 to infinity of nx^(2n))

 

[eok20]

Try to first find an equation for sum n*x^n = x*sum n*x^(n-1) using integration/differentiation.