Question

1/1*2+1/2*3+1/3*4······+1/99*100简便算，！要算式思路

Answer 1

1/1*2+1/2*3+1/3*4······+1/99*100
=1/(1×2)+1/(2×3)+....+1/(99×100)
=(1-1/2)+(1/2-1/3)+.......+(1/99-1/100)
=1-1/2+1/2-1/3+.......+1/99-1/100
=1-1/100
=99/100

类似：1/[a*(a+n)]=(1/n)*[1/a-1/(a+n)]

例子：
1/56=1/(7*8)=1/7-1/8
1/12=1/(2*6)=(1/4)*[1/2-1/6]
....................
等等

以上的式子是很重要的，能记住对解这类的题是有帮助的~
希望能帮到你~~
如果满意，请采纳一下拉~~谢谢啊~~~

Answer 2

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