求和函数((2n+1)*x^2n)/2^2n+1从0到无穷大,

Question

求和函数((2n+ 1)*x^2n)/2^2n+1
从0到无穷大,

Answer 1

先求收敛域,你自己求吧
原式=求和:1/2*(2n+1)*(x/2)^2n=求和:[(x/2)^2n+1]'=[求和：(x/2)^2n+1]'=[x/(2-x^2/2)]'