MathDB
2016 Guts #23

Source:

December 24, 2016

Problem Statement

Let t=2016t = 2016 and p=ln⁡2p = \ln 2. Evaluate in closed form the sum ∑k=1∞(1−∑n=0k−1e−ttnn!)(1−p)k−1p. \sum_{k=1}^{\infty} \left( 1-\sum_{n=0}^{k-1}\frac{e^{-t}t^{n}}{n!} \right) \left(1-p\right)^{k-1}p.
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