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Let $n_1,\ldots,n_{m+1}$ be natural numbers, such that their sum is equal to some constant $C$.

I would like to calculate $ 1+\frac{1}{\sqrt{n_ 1}}\left( 1+ \frac{1}{\sqrt{n_2}}+\frac{1}{n_2\sqrt n_3}+\cdots+\frac{1}{n_2\cdots n_m\sqrt{n_{m+1}}} \right) $

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    Do you have some reason to believe that quantity really depends only on $C$? Have you done any numerical experiments to test this? For example, does $n_1=1$, $n_2=4$, $n_3=9$ give the same answer as $n_1=4$, $n_2=9$, $n_3=1$? In both cases, $C=14$.2012-04-18

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