巧算1道数学题1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?
问题描述:
巧算1道数学题
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?
答
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10=1-1/10=9/10
答
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/(9*10)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9+1/9-1/10 (括号拆开,中间抵消掉 )
=1-1/10
=9/10