## 2016 Putnam Problem B1

2016 Putnam B1. Let $x_0, x_1, x_2, \dots$ be the sequence such that $x_0 = 1$ and for $n \geq 0$, $x_{n+1} = \ln(e^{x_n} - x_n)$ (as usual, the function $\ln$ is the natural logarithm.

Show that the infinite series $x_0 + x_1 + x_2 + \dots$ converges and find its sum.