Its GIF not GF

Calculus Level 4

If function \(f\) is defined as \( f(n)= \lfloor \sqrt{n}+0.5 \rfloor \), find the value of \[ \left\lfloor \displaystyle \sum_{n=1}^{\infty}\frac{2^{f(n)}+2^{-f(n)}}{2^{n}} \right\rfloor. \]

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