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## Homework Statement

Hi, i had to solve a some series and i had no problem except for this one

[tex]\sum\frac{6}{4n^2+1}[/tex] from 1 to infinity

## The Attempt at a Solution

i've tried to do it by simple fractions didn't work, it's no geometric,hipergeometric, telescopic.

All exercices had "nice" solutions meaning they were round numbers or fractions, so i solved this one with mathematica and gave me an "ugly" solution wich is

[tex]\frac{3}{2}\left(-2 + \pi coth (\frac{\pi}{2})\right)[/tex]

So i though maybe is a typo and its actually [tex]\sum\frac{6}{4n^2-1}[/tex] from 1 to infinity, so i did this one by simple fractions and gave me 3, but i still want to learn how to solve the original, i wanna know how can be the coth function in the solution!

Thx for the help