If $f(x)=\frac{{2}^{x}}{{2}^{x}+\sqrt{2}},x\in R,$ then $\sum _{k=1}^{81}f\left(\frac{k}{82}\right)$ is equal to: [JEE Main 2025, 28 Jan (Shift 1)]

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If \(f(x)=\frac{{2}^{x}}{{2}^{x}+\sqrt{2}},x\in R,\) then \(\sum _{k=1}^{81}f\left(\frac{k}{82}\right)\) is equal to: [J…