For the periodic function given by $f(x)=\left\{\begin{array}{ll}-2, & -\pi<x<0 \\ 2, & 0<x<\pi\end{array}\right.$ with $f(x+2 \pi)=f(x),$ using
Fourier series, the sum $s=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\cdots$ converges to
(A) 1
(B) $\frac{\pi}{3}$
(C) $\frac{\pi}{4}$
(D) $\frac{\pi}{5}$

Question ID - 155901 | SaraNextGen Top Answer

For the periodic function given by $f(x)=\left\{\begin{array}{ll}-2, & -\pi<x<0 \\ 2, & 0<x<\pi\end{array}\right.$ with $f(x+2 \pi)=f(x),$ using
Fourier series, the sum $s=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\cdots$ converges to
(A) 1
(B) $\frac{\pi}{3}$
(C) $\frac{\pi}{4}$
(D) $\frac{\pi}{5}$