(1) (15 points) Consider the

2\\\\pi

-periodic function

f(x)

defined on

-\\\\pi ,\\\\pi

by the for-\ mula

f(x)=cos((x)/(2))

.\ (a) Find the Fourier series expansion of

f(x)

.\ (b) Use part (a) to find the sum of the following series:\

A=\\\\sum_(n=1)^(\\\\infty ) ((-1)^(n+1))/(4n^(2)-1), and ,B=\\\\sum_(n=1)^(\\\\infty ) (1)/(4n^(2)-1).

(1) (15 points) Consider the 2-periodic function f(x) defined on [,] by the formula f(x)=cos(2x). (a) Find the Fourier series expansion of f(x). (b) Use part (a) to find the sum of the following series: A=n=14n21(1)n+1andB=n=14n211