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

Sep 28, 2014

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

Therefore,

pi-pi^2/{2!}+{pi^4}/{4!}-{pi^6}/{6!}+cdots

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

$= \pi - 1 + \left(- 1\right) = \pi - 2$

I hope that this was helpful.