1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/13 08:51:03
![1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)](/uploads/image/z/15251252-68-2.jpg?t=1%2F%281%C3%972%29%2B1%2F%282%C3%973%29%2B1%2F%283%C3%974%29%2B%26%238943%3B%2B1%2F%2899%C3%97100%29)
x)30<ZlȲPP(l16~\KK α
ZFt@kycu ƽi_\gu
o=h#v$ (b
1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
=1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100
(1/(1*2)=1-1/2,1/(2*3)=1/2-1/3,……)
原式=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100
=99/100