Fourier Series of Periodic Function f(x) | GATE Civil Engineering

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Civil Engineering > GATE 2025 SET-1 > Fourier Series

Which one of the following options is the correct Fourier series of the periodic function f(x) described below:

A

f(x)=k/2 + 2k/π(cos(π/2)x - (1/3)cos(3π/2)x + (1/5)cos(5π/2)x -+···)

B

f(x)=k/2 + 2k/π(sin(π/2)x - (1/3)sin(3π/2)x + (1/5)sin(5π/2)x -+···)

C

f(x)=k + 4k/π(cos(π/2)x - (1/3)cos(3π/2)x + (1/5)cos(5π/2)x -+···)

D

f(x)=k + 4k/π(sin(π/2)x - (1/3)sin(3π/2)x + (1/5)sin(5π/2)x -+···)

Correct : a

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