How to prove: \sum_{n=1}^\infty\frac{1}{16n^2-16n+3}=\frac{\pi}{8}

dristauwaz

dristauwaz

Answered question

2022-02-24

How to prove:
n=1116n216n+3=π8

Answer & Explanation

Halle Hansen

Halle Hansen

Beginner2022-02-25Added 5 answers

n=1116n216n+3=18n=1(1n341n14)
=18n=101(xn74xn54)dx
=1801n=1(xn74xn54)dx
=1801(x341xx141x)dx
=1801(x34x141x)dx
=18011(x+1)x34dx
=18[4arctan(x4)]01
=π8
n=1116n216n+3=π8

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