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

Sep 12, 2014

Since the Maclaurin series
1-x^2/{2!}+x^4/{4!}-x^6/{6!}+cdots=cosx,
1-(pi/4)^2/{2!}+(pi/4)^4/{4!}-(pi/4)^6/{6!}+cdots=cos(pi/4)=1/sqrt{2}.