1/2+1/6+1/12+1/20+……+1/56=?
问题描述：
1/2+1/6+1/12+1/20+……+1/56=?
答
5
答
1/2+1/6+1/12+1/20+……+1/56
＝1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+....+(1/7-1/8)
=1/2+1/2-1/8
=1-1/8
=7/8
答
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/(1x2) +1/(2x3) +1/(3x4)+...+1/(7x8)
=(1- 1/2) +(1/2-1/3)+...+(1/7-1/8)
=1-1/8
=7/8
答
分母2=1*2 6=2*3, 12=3*4 20=4*5 56=7*8
分数进行拆项
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
...
1/56=1/7-1/8
全部相加，等式右边中间项全部抵消
1/2+1/6+1/12+1/20+……+1/56=1-1/8=7/8