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 Post subject: Putnam 2016 B1Posted: Mon Dec 05, 2016 6:06 pm

Joined: Sat Nov 14, 2015 6:32 am
Posts: 157
Location: Melbourne, Australia
Let $x_0, \; x_1, \; x_2, \; \dots$ be the sequence such that $x_0=1$ and for $n \geq 0$ it holds that:

$$x_{n+1}=\ln(e^{x_n}-x_n)$$

Show that the infinite series $\sum \limits_{n=0}^{\infty} x_n$ converges and evaluate its value.

_________________
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$

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