August 16th, 2018, 04:22 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: $\displaystyle \lim_{n\to\infty}\frac{ba}{n} \sum_{k=1}^{n}f(x_k) = \int_a^b f(x) dx$ ... 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 06:22 AM. 
August 16th, 2018, 10:47 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,476 Thanks: 2039 
Are you sure that the $n^4$ in the denominator is correct?

August 17th, 2018, 01:53 AM  #3 
Newbie Joined: Nov 2016 From: Bulgaria Posts: 6 Thanks: 0 
Yes, positive


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problem, riemann, sums 
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