ICode9

Putnam试题 For any positive integer n let denote the closest integer to $\sqrt{n}$，Evaluate $$\sum_{n=1}^{∞}\frac{2^{<n>}+2^{-<n>}}{2^{n}}$$   Solution: Since $(k-\frac{1}{2})^{2}=k^{2}-k+\frac{1}{4}$ and $(k+\frac{1}{2})^{2}=k^{2}+k+\fra