A discrete random variable X has the probability mass function

$\displaystyle P(X=x)=\left{c(0.90)^{x} \quad \text{if x = 0,2,4,6,8,...}$

and

$\displaystyle P(X=x) = 0 \quad \text{otherwise}$

What must be the value of the constant c in order for this to be a legitimate p.m.f.?

I would think that,

$\displaystyle \sum_{x=0}^{\infty}c(0.9)^{x} = 1, \quad \text{Where x is only even values}$

But how does one solve for c?

Does

$\displaystyle \sum(0.9)^{x}$

decompose into a more convient form somehow?

Thanks again!