Suppose P(Yn<=y)=1-e^(-2ny/(n+1)) for all y>0. Prove that Yn converges in distribution to Y where Y has the exponential distribution for some lambda >0 and compute lambda.

so for this i get

[lim n->inf] 1-e^(-(2ny)/(n+1)) -> 1-e^(-y*lambda)

I'm not sure how to prove the convergence here...

Is it enough to say that lambda = (2n)/(n+1) ?

since 2n > n+1, the result will always be > 1, which is what lambda can be.