I'm trying to find the value of the following series $\displaystyle \sum _{n=1}^{\infty } \frac{1}{n}\left(\frac{np}{p+n}\right)^{n+1}$ where 0<p<1. Any thoughts? Thanks.
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Even here the problem hasn't be solved. With the fact that $\displaystyle 0<p<1$, I guess you work on probabilities. Maybe you don't have to compute the sum but only establish some properties.
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