怎样求:1-1/2+1/3-1/4+1/5-1/6+……+1/(2n-1)-1/(2n)的和?

问题描述:

怎样求:1-1/2+1/3-1/4+1/5-1/6+……+1/(2n-1)-1/(2n)的和?
大侠,最后一步怎么变的?

当n=>∞时S=ln21-1/2+1/3-1/4……+1/2n =1+1/2+1/3+1/4……+1/2n-2(1/2+1/4+……+1/2n) =1/(n+1)+1/(n+2)+……1/2n =1/n(1/(1+1/n)+1/(1+2/n)+……+1/(1+n/n) =1/(1+x)[从0积到1]=ln2