1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法

来源：学生作业帮助网编辑：六六作业网时间：2024/12/19 05:15:25

1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法1+1/(1+2)+1/

1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法
1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法

1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法
1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)
=2/(1×2)+2/(2×3)+2/(3×4)+.+2/(100×101)
=2[1/(1×2)+1/(2×3)+1/(3×4)+.+1/(100×101)]
=2(1-1/2+1/2-1/3+1/3-1/4+.+1/100-1/101)
=2(1-1/101)
=200/101