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August 16th, 2018, 05:22 AM   #1
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Riemann sums problem

Hello!

I am struggling with approaching the following problem:
$\displaystyle \lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{\sqrt{n^4 + k^2}}$

I know that I probably have to use something like the following:
$\displaystyle \lim_{n\to\infty}\frac{b-a}{n} \sum_{k=1}^{n}f(x_k) = \int_a^b f(x) dx$

... but currently I'm in a block and can't seem to find my way around this problem.

Any help will be greatly appreciated.

Last edited by skipjack; August 16th, 2018 at 07:22 AM.
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August 16th, 2018, 11:47 AM   #2
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Are you sure that the $n^4$ in the denominator is correct?
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August 17th, 2018, 02:53 AM   #3
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Yes, positive
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