Convergence in probability not L2

Let $X_{1},X_{2},…$ be a sequence of independent random variables with $P(X_{n}=n)=\dfrac{1}{n^{2}}=1-P(X_{n}=0)$, for $n=1,2,…$. Consider the following statements. $P$: $\{X_{n}\}$ converges in mean-square to $0$. $Q$: $\{X_{n}\}$ converges in probability to $0$. Then