Band Of Brothers : L\\\\\\\\’Enfer Du Pacifique Saison 1 VF TORRENT ○ DOWNLOAD (Mirror #1)
Band Of Brothers : L\\\\\\\\’Enfer Du Pacifique Saison 1 VF TORRENT
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. Band Of Brothers : L\\\\\\\’Enfer Du Pacifique Saison 1 VF TORRENT
Torrent Les Experts Manhattan Saison 4 French – Band Of Brothers. Si leurs courages ne sont plus rusés, leurs lancs n’en finissent pas. (Les Explorations de l’Ande, dans la Monnaie et l’Univers,.Q:
Is it possible to evaluate $sumlimits_{i=1}^{infty}frac{sqrt{i}}{sqrt{i+1}+sqrt{i}}$
Is it possible to evaluate the following series?
$$sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i+1}+sqrt{i}}$$
I’m quite sure that it converges but I don’t know how to evaluate it.
Thanks.
A:
I think this is a bit of a loose end (at least at first glance).
The series $sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i+1}+sqrt{i}}$
can be rewritten as $sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i+1}}-sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i}}$.
The first series diverges by the ratio test (as the terms are decreasing) and the second converges.
But that second series can be rewritten as
$sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i+1}+sqrt{i}}$ $=frac{1}{2}sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i+1}}$ $-frac{1}{2}sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i}}$ $=frac{1}{2}left(1-1right)sum_{i=1}^{infty}frac{sqrt{i}}{sqrt{i+1}}$ $
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