1/(1*2)+1/(2+3)+1/(3*4)+...+1/(99*100)

Question

就是分子都是1，分母分别是1*2 2*3 3*4 4*5 5*6...一直到99*100 这些分数加起来等于多少 大约说下算法 谢谢啦

Answer 1

原式=1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100=1-1/100=0.99

Answer 2

=1-1/2+1/2-1/3+1/3-1/4.....+1/99-1/100
=99/100

Answer 3

∵1/(2×3)=1/6
1/2-1/3=3/6-2/6=1/6

1/(3×4)=1/12
1/3-1/4=4/12-3/12=1/12
...............

∴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

Answer 4

对 就是上面的这个 99/100