# A problem by Anish Roy

Level pending

For any positive integer $$n$$, let $$\langle{n}\rangle$$ denote the closest integer to $$\sqrt{n}$$. Evaluate $\displaystyle \sum_{n=1}^{\infty} \frac{2^{\langle{n}\rangle}+2^{-\langle{n}\rangle}}{2^{n}}$

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