Find the radius of convergence for ∞ n=1 n! -xn. 1·3·5· ... · (2n – 1) · (2n – 1) x²

show that the fourier series of the function ?(?) = |?| ?? [−?, ?] is :

Use generating functions to solve an 2an 1+1 for n ≥ 1 where ao = 0. [At most 1 point if you don't use generating func- tions.] =

n+1 (3) Construct a function f(x) such that for any integer n e Z, the integral f(x)dr is improper and convergent.