- #1
springo
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Homework Statement
I need to find the following:
[tex]\lim_{n\rightarrow\infty}\left(\frac{1^2+2^2+3^2+...+n^2}{n^3} \right)[/tex]
Homework Equations
The Attempt at a Solution
I know I could do the sum of the series to find the result but I would like to use Riemann sums.
I think I have to start by writing the limit as:
[tex]\lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{n}\left(\frac{k}{n} \right)^2[/tex]
However, I'm not sure how to continue.
Thanks for your help.
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