Question

1-1/2+1/3-…+1/n求和

1-1/2+1+3-1/4+1/5+……1/n求和
1-1/2+1+3-1/4+1/5+……1/n总之,奇数的倒数是加,偶数的倒数是减,求第n项和

Answer 1

当n=>∞时
和=ln2
1-1/2+1/3-1/4+1/5-1/6+……+1/（2n-1）-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