How can I calculate \sum_{n=1}^{n=1}\frac{(-1)^n}{16n^2-1} using the Fourier series?

iristh3virusoo2

iristh3virusoo2

Answered question

2022-02-24

How can I calculate
n=1n=1(1)n16n21
using the Fourier series?

Answer & Explanation

Elena Ray

Elena Ray

Beginner2022-02-25Added 4 answers

|sin(x)|=2π4πn=1cos(2nx)4n21
|sin(π4)|=2π4πn=1cos(πx2)4n21
=2π4πn=even(1)n24n21
(n2m)=2π4πm=1(1)m16m21
n=1(1)n16n21=2π224π

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