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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

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