数学问题(最简单的+-*/）

1+（2+1/6）+（3+1/12）+……+（8+1/72)
= 1+2+3+......+8+(1/6+1/12+......+1/72)
=(1+8)*8/2+(1/2-1/3)+(1/3-1/4)+......+(1/8-1/9)
=36+1/2-1/9
=36又7/18

1/(2*5)+1/(3*6）+1/(4*7)+……+1/（7*10）
=[(1/2-1/5)+(1/3-1/6)+(1/4-1/7)+(1/5-1/8)+(1/6-1/9)+(1/7-1/10)]÷3
=(1/2+1/3+1/4-1/8-1/9-1/10)÷3
=[(1/2-1/8)+(1/3-1/9)+(1/4-1/10)]÷3
=(3/8+2/9+3/20)÷3
=1/8+2/27+1/20
=269/1080