Hi I have a question:

So suppose that

P(Y_{n}= k) = (1 - 2^{-n-1})^{-1}/ 2^{k+1 }for k=0,1,...n.

And Y~ geo(1/2)

How do I show that Y_{n}converges in distribution to Y?

I know I have to incorporate the PMF of the geometric distribution which is p_{x}(k) = P(X=k) = (1-p)^{k-1}p