Calculus Quiz

Calculus Level 5

\[f(x)=\sum_{k=1}^{\infty}\frac{\sin(kx)}{k^2}\]

Find the value of \(x\), with \(0< x\leq 2\pi\), where \(f(x)\) attains its maximal value. Write \(x=\frac{a\pi}{b}\), where \(a\) and \(b\) are coprime positive integers, and enter \(a+b\).

If you come to the conclusion that no such \(x\) exists, enter 666.

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