Question

3分之1加6分之1加10分之1加15分之1加21分之一加28分之1加36分之1+45分之1 =? 用简便方法计算 要完整过程

Answer 1

1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
=(1/3+1/6)+(1/10+1/15)+(1/21+1/28)+(1/36+1/45)
=(2+1)/6+(3+2)/30+(4+3)/84+(5+4)/180
=1/2+1/6+1/12+1/20
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/5
=4/5

Answer 2

转化一下就行了。
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45

=2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=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)]
=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)
=2*(1/2-1/10)
=2*(12/20)
=12/10
=6/5
其实不难，只是有点绕。