Let $X_1, X_2, ..., X_n, ...$ be independent random variables. Assume that for each $n$, the random variable $X_n$ is distributed uniformly on $[0,n]$. Find a sequence $a_n$ such that $(X_1^2 + ... + X_n^2) / a_n$ converges to $1$ in probability.
I honestly have no idea how to start this problem. The only things that come to mind is to make a Law of Large Numbers type argument or to try to brute force it by using the definition of convergence in probability.