GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/30

Question 30 (Textile Engineering & Fibre Science)

The fourier series of periodic function $f(x)=\begin{cases} -k & -\pi<x<0 \\ k & 0<x<\pi \end{cases}$ and $f(x+2\pi) = f(x)$ is given by $\frac{4k}{\pi}\left ( sinx + \frac{1}{3}sin 3x +\frac{1}{5}sin5x +….. \right )$ . Then the value of $\frac{4}{\pi}\left ( 1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+….. \right )$ is equal to __________.

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