求教六年级一道简算题,要有分析过程
问题描述：
求教六年级一道简算题,要有分析过程
111 11
____ + ______ +_______+.+______ +_______
1*3 3*55*717*1919*21
问题没有表述清楚，原题可以表述为1/(1*3)+1/(3*5)+1/(5*7)+....+1/(17*19)+1/(19*21)
答
1/(1*3)+1/(3*5)+1/(5*7)+.+1/(17*19)+1/(19*21)
=1/2*2{1/(1*3)+1/(3*5)+1/(5*7)+.+1/(17*19)+1/(19*21)}2
=1/2{2/(1*3)+2/(3*5)+2/(5*7)+.+1/(17*19)+2/(19*21)}
=1/2*{(1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/19-1/21)}
=1/2*{1-1/21}
=10/21