P(Yn=k)= ( (1-2^(-n-1))^(-1) )/ 2^(k+1) for k=0,1,2,...,n. The random variable Y has the geometric distribution where lambda is 1/2. How can I prove that {Yn} converges in distribution to Y?

Any help is appriciated.

I get fY(y)=1/2^(y+1)

but how do I prove the convergence?