Question

1/6+1/12+1/20+30/1+40/1的简便算法

Answer 1

我觉得你的题目打错了

题目可能是

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

但都是用裂项法...

1)(没打错)

原式=1/6+1/12+1/20+1/30+1/40

=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/40

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/40

中间很多项都抵消

So 原式=1/2-1/6+1/40=43/120

2)打错了

原式=1/6+1/12+1/20+1/30+1/42

=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

中间很多项都抵消

So 原式=1/2-1/7=5/14