My Math Forum Riemann sums problem

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 August 16th, 2018, 05:22 AM #1 Newbie   Joined: Nov 2016 From: Bulgaria Posts: 6 Thanks: 0 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.
 August 16th, 2018, 11:47 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,882 Thanks: 1835 Are you sure that the $n^4$ in the denominator is correct?
 August 17th, 2018, 02:53 AM #3 Newbie   Joined: Nov 2016 From: Bulgaria Posts: 6 Thanks: 0 Yes, positive

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