Question

How do you use a power series to find the exact value of the sum of the series `1-pi^2/(2!)+pi^4/(4!) +pi^6/(6!) + …` ?

Answer 1

Since

`1-x^2/{2!}+{x^4}/{4!}-x^6/{6!}+cdots=cosx`,

`1-pi^2/{2!}+pi^4/{4!}-pi^6/{6!}+cdots=cos(pi)=-1`

I know that it is different from what you have, but I have a feeling that this is what you meant to ask.