MathDB

Putnam 2001 B3

Source:

February 27, 2012

Putnamcollege contests

Problem Statement

For any positive integer

n

, let

\left< n \right>

denote the closest integer to

\sqrt {n}

. Evaluate:

\displaystyle\sum_{n=1}^{\infty} \dfrac {2^{\left< n \right>} + 2^{- \left< n \right>}}{2^n}