Why isn't this zero? Find the limit 1^2/n^3+2^2/n^3+...+n^2/n^3. Reddit calculus r/HomeworkHelp

We will evaluate the limit of 1^2/n^3+2^2/n^3+3^2/n^3+...+(n-1)^2/n^3+1/n as n goes to infinity. You might notice that this is a limit of a Riemann sum, which we can convert to an integral and then evaluate. However, I will also show you the original way to evaluate this kind of limit by using 1^2+.2^2+...+n^2=n(n+1)(2n+1)/6. This is from Reddit r/HomeworkHelp
Reddit: LNT0uE8BjL
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