Question

1/1x2+1/2x3+1/3x4+.........1/98x99+1/99x100=?

要注明运算过程

Answer 1

这道题的分子都是1 通过观察可以发现
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
原式＝1-1/2+1/2-1/3+1/3-1/4+1/4+……+1/98-1/100
＝99/100
这道题的解法叫做裂项或者拆分 是初一学习的内容

Answer 2

通过观察可以发现
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4 ~~~
1/N(N+1)=1/N-1/(N+1)
所以1/1x2+1/2x3+1/3x4+.........1/98x99+1/99x100
=(1-1/2) + (1/2-1/3) + (1/3-1/4) + (1/98-1/99) + (1/99-1/100)
=1 - 1/100
=99/100 这道题的解法叫做裂项或者拆分

Answer 3

99/100

Answer 4

1/1x2+1/2x3+1/3x4+.........1/98x99+1/99x100
=(1-1/2) + (1/2-1/3) + (1/3-1/4) + (1/98-1/99) + (1/99-1/100)
=1 - 1/100
=99/100

Answer 5

一百分之九十九。
1-1/2+1/2-1/3.........+1/99-1/100
=1-1/100
=99/100

Answer 6

1/1x2+1/2x3+1/3x4+.........1/98x99+1/99x100
=(1-1/2) + (1/2-1/3) + (1/3-1/4) + (1/98-1/99) + (1/99-1/100)
=1 - 1/100
=99/100