2楼windyma
(......)
发表于 2011-1-27 23:39
只看此人
1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
……
1/(9*10)=1/9-1/10
所以,
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+……+1/(9*10)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10
=1-1/10
=9/10
9/10+1/10=1
所以这10个分母就是2/6/12/20/30/42/56/72/90和10.