The score series calculation problem should be simplified, 1 1 1 1 ---------- + ---------- + ----------- +………… +--------------- 1*2*3 2*3*4 3*4*5 98*99*100

The score series calculation problem should be simplified, 1 1 1 1 ---------- + ---------- + ----------- +………… +--------------- 1*2*3 2*3*4 3*4*5 98*99*100

The original formula = 1 / 2 * [1 / (1 * 2) - 1 / (2 * 3) + 1 / (2 * 3) - 1 / (3 * 4) +... + 1 / (99 * 100)] = 1 / 2 * [1 / (1 * 2) - 1 / (99 * 100)] = 1 / 2 * [1 / 2-1 / 9900] = 1 / 2 * (4989 / 9900) = 4989 / 9900

A few calculation problems,
First: (1 + 1 / 2) * (1 + 1 / 3) * (1 + 1 / 4) * （1+1/2007）=
The second way: (- 1) + - 1's square + (- 1's cube +...) +The power of (- 1)=
The third course: 1 / 1 * 2 + 1 / 2 * 3 + 1 / 3 * 4 + +1/2007*2008=

First:
（1+1/2）*（1+1/3）*（1+1/4）*…… （1+1/2007）
=3/2*4/3*.*2008/2007
=2008/2
=1004
Second:
(- 1) + - 1's square + (- 1's cube +...) +The power of (- 1)
=(-1)+1+(-1)+1+.+1
=0
Third:
1/1*2+1/2*3+1/3*4+…… +1/2007*2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008
=1-1/2008
=2007/2008

A few calculation problems,
1.（2/3-1/2)-(1/3-5/6)
2.2.4-(-3/5)+(-3.1)+4/5
3,(-6/13)+(-7/13)-(-2)
4.3/4-(-11/6)+(-7/3)

1. The original formula = 2 / 3-1 / 2-1 / 3 + 5 / 6 = 4 / 6-3 / 6-2 / 6 + 5 / 6 = 4 / 6 = 2 / 3
2. The original formula = 2.4 + 0.6-3.1 + 0.8 = 0.7
3. The original formula = - 6 / 13-7 / 13 + 2 = - 1 + 2 = 1
4. The original formula = 9 / 12 + 22 / 12-28 / 12 = 3 / 12 = 1 / 4