1/2+1/6+1/12+1/20+1/30+1/42

题目

1/2+1/6+1/12+1/20+1/30+1/42
=
注：要层等式,并且要有过程,不要直接写出答案的,能讲讲怎么算的更好,

答案

可以变形,把第二位的6看成是2乘以3.后面依次类推.
原式=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6
=1-1/7
=6/7