Suppose the number of children N of a random family satifies P(N=n)=(3/5)[(2/5)^n] where n=0,1,2,... Compute E(N).

I went through the math and I come up with 1, which is the probability space. So, I know I'm not going about this the right way.

$\displaystyle E(N=n)=\frac{3}{5}(\frac{2}{5})^0 + \frac{3}{5}(\frac{2}{5})^1 + \frac{3}{5}(\frac{2}{5})^2 + ...$

$\displaystyle =\sum_{n=0}^{\infty}\frac{3}{5}(\frac{2}{5})^n$

$\displaystyle =\frac{3}{5}\sum_{n=0}^{\infty}(\frac{2}{5})^n$

$\displaystyle =\frac{3}{5}\frac{5}{3}$

$\displaystyle =1$

Could somone point out the basic understanding of expected value that I seem to be missing in this problem?