# Determine the sum of the series (pi^2)/(4^2 2!)−(pi^4)/(4^4 4!)+(pi^6)/(4^6 6!)−(pi^8)/(4^8 8!)+...

I want to determine the sum of the series
$\frac{{\pi }^{2}}{{4}^{2}2!}-\frac{{\pi }^{4}}{{4}^{4}4!}+\frac{{\pi }^{6}}{{4}^{6}6!}-\frac{{\pi }^{8}}{{4}^{8}8!}+\cdots$
What I am trying to do is to consider that
$\mathrm{cos}\left(x\right)=1-\frac{{x}^{2}}{2!}+\frac{{x}^{4}}{4!}-\frac{{x}^{6}}{6!}+...$
then
$-\mathrm{cos}\left(x\right)+1=\frac{{x}^{2}}{2!}-\frac{{x}^{4}}{4!}+\frac{{x}^{6}}{6!}-...$
Up to this point the expression resembles the one I am looking for, however I have not been able to find the final result, any help?
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Quinten Cervantes
It sounds like you are adding
$\sum _{n=1}^{\mathrm{\infty }}\left(-1{\right)}^{2n+1}\frac{\left(\pi /4{\right)}^{2n}}{\left(2n\right)!}$
which will fit into that cosine flavor when you set $x=\pi /4$...