Question

一道简便计算

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

Answer 1

解答这类简便算法题的关键是分解
将原来算式里的各个数字分解为不同的项，
既简便算法原理：化加法为减法
所以可得到:
原式
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)...+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10
=0.9

Answer 2

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=0.9

Answer 3

直接在草稿上进行同分可得结果：9/10