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) $