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March 30th, 2017, 01:28 AM   #1
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series sum

Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=1}\frac{1}{(k-1)\sqrt{k}+k\sqrt{k+1}}$
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March 30th, 2017, 06:25 PM   #2
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Are you sure it's typed correctly? The summand is undefined at k = 1.
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March 31st, 2017, 02:23 AM   #3
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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....
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Last edited by Benit13; March 31st, 2017 at 03:02 AM.
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April 6th, 2017, 08:21 PM   #4
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Sorry friends actually original question is

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Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=1}\frac{1}{(k-1)\sqrt{k}+k\sqrt{k-1}}$
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April 7th, 2017, 01:08 AM   #5
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Sorry friends actually original question is
That one is undefined at k=1.
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April 8th, 2017, 04:15 AM   #6
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Sorry friends correct question is
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Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=2}\frac{1}{(k-1)\sqrt{k}+k\sqrt{k-1}}$
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April 8th, 2017, 08:11 AM   #7
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Big hint: $\dfrac{1}{(k-1)\sqrt{k}+k\sqrt{k-1}} = \dfrac{1}{\sqrt{k-1}} - \dfrac{1}{\sqrt{k}}$.
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