求和,Sn=x^2+x^4+x^6+…+nx^2n

问题描述:

求和,Sn=x^2+x^4+x^6+…+nx^2n

Sn=x^2+x^4+x^6+…+x^2n ...(1)
x^2*Sn=x^4+x^6+…+x^2n+x^(2n+2) ...(2)
(2)-(1)得:(x^2-1)*Sn=x^(2n+2)-x^2
Sn=(x^(2n+2)-x^2)/(x^2-1)