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

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

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

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