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:作业帮 时间:2024/07/04 22:27:18
![1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=小学解法](/uploads/image/z/4004735-23-5.jpg?t=1%2B1%2F%281%2B2%29%2B1%2F%281%2B2%2B3%29%2B%E2%80%A6%2B1%2F%281%2B2%2B3%2B4%2B%E2%80%A6%2B100%29%3D%E5%B0%8F%E5%AD%A6%E8%A7%A3%E6%B3%95)
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