Let Yn = sum of n i.i.d RVs/ sqrt(n), what happens to Yn as n --> inf?

Question

This is the complete description of the question. As you can see the form of Yn is very close to that of CLT, but not exactly the same. So how should I approach the problem in this case? I do know the E(Xi) is 1/lambda, and Var(Xi) is 1/lambda^2 and so Var(Yn) is 1/lambda^2 and E(Yn) is sqrt(n)/lambda from the question.

Thanks!