1/2+1/(2+4)+1/(2+4+6)+...1/(2+4+6+...2n),求和

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/16 06:33:11
1/2+1/(2+4)+1/(2+4+6)+...1/(2+4+6+...2n),求和

1/2+1/(2+4)+1/(2+4+6)+...1/(2+4+6+...2n),求和
1/2+1/(2+4)+1/(2+4+6)+...1/(2+4+6+...2n),求和

1/2+1/(2+4)+1/(2+4+6)+...1/(2+4+6+...2n),求和
1/2+1/(2+4)+1/(2+4+6)+...1/(2+4+6+...2n)
=1/(1×2)+1/(2×3)+1/(3×4)+.+1/[n(n+1)]
=1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)