1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45=几?

1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45=几?
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45=几?

1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45=几?
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

怎么又出现一次啊。
思路：你可以观察分母，它的相邻两分母之差可以组成一个等差数列，有了这一个数列的方程在解原列的前十八项之和还不容易吗?

4/5

1/3+(1/2-1/3)+(1/2-1/5)/3+1/15+(1/3-1/7)/4+1/28+(1/4-1/9)/5+1/45
=1/2+1/6+1/12+1/20
=1/2+1/2-1/3+1/3-1/4+1/4-1/5
=4/5