# Central Limit Theorem- Lapunow, Linderberg

I have a task: $$(X_n)_{n>=1}$$ are independent. $$P(X_n=0)=1/n$$ and $$P(X_n=2n)=1-1/n$$. Check the weak convergence $$\frac{X_1+X_2+X_3+....+X_n}{n}-n$$. I tried use the Lapunow theorem or Linderberg theorem to $$X_{n,k}=\frac{X_k}{n}-1$$. But the variance converges to infinity.