Question

一道数学题,要理解的方法,这是是带分数：1*1/2+2*1/6+3*1/12+4*1/20+5*1/30+6*1/42+

Answer 1

1/2=1/1-1/2

1/6=1/2-1/3

1/12=1/3-1/4

1/20=1/4-1/5

1/30=1/5-1/6

1/42=1/6-1/7

1/56=1/7-1/8

原式化简=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

+1/5-1/6 +1/6-1/7+1/7-1/8

+1/6-1/7+1/7-1/8

+1/7-1/8

这样一行一行的算下来,再加到一起.