## Problem of the Day #268: An Infinite Series
*December 12, 2011*

*Posted by Saketh in : potd , add a comment*

Let $a_1 = \frac{1}{2011}$ and let $a_{n+1} = a_n \cdot (a_n+1)$. Evaluate

$$\frac{1}{a_1+1}+\frac{1}{a_2+1}+\frac{1}{a_3+1}+\cdots$$