Putnam 2016 B1
Posted: Mon Dec 05, 2016 6:06 pm
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.
$$x_{n+1}=\ln(e^{x_n}-x_n)$$
Show that the infinite series $\sum \limits_{n=0}^{\infty} x_n$ converges and evaluate its value.