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 March 30th, 2017, 01:28 AM #1 Senior Member   Joined: Jul 2011 Posts: 392 Thanks: 15 series sum Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=1}\frac{1}{(k-1)\sqrt{k}+k\sqrt{k+1}}$
 March 30th, 2017, 06:25 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,475 Thanks: 886 Math Focus: Elementary mathematics and beyond Are you sure it's typed correctly? The summand is undefined at k = 1.
March 31st, 2017, 02:23 AM   #3
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Quote:
 Originally Posted by greg1313 Are you sure it's typed correctly? The summand is undefined at k = 1.
I get summand = $\displaystyle \frac{1}{0 + \sqrt{2}} =\frac{1}{\sqrt{2}}$ when k=1.

As for the evaluation of the summand for all k? Hmmm....

Last edited by Benit13; March 31st, 2017 at 03:02 AM.

April 6th, 2017, 08:21 PM   #4
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Sorry friends actually original question is

Quote:
 Originally Posted by panky Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=1}\frac{1}{(k-1)\sqrt{k}+k\sqrt{k-1}}$

April 7th, 2017, 01:08 AM   #5
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Quote:
 Originally Posted by panky Sorry friends actually original question is
That one is undefined at k=1.

April 8th, 2017, 04:15 AM   #6
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Sorry friends correct question is
Quote:
 Originally Posted by panky Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=2}\frac{1}{(k-1)\sqrt{k}+k\sqrt{k-1}}$

 April 8th, 2017, 08:11 AM #7 Global Moderator   Joined: Dec 2006 Posts: 16,949 Thanks: 1256 Big hint: $\dfrac{1}{(k-1)\sqrt{k}+k\sqrt{k-1}} = \dfrac{1}{\sqrt{k-1}} - \dfrac{1}{\sqrt{k}}$. Thanks from panky

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