简便运算1/（2*5）+1/（3*5）+1/(8*11)+……+1/（20*23）=
问题描述：
简便运算1/（2*5）+1/（3*5）+1/(8*11)+……+1/（20*23）=
答
1/2-1/5=3/（2*5)
1/5-1/8=3/（5*8）...
1/（2*5）+1/（3*5）+1/(8*11)+……+1/（20*23）
=1/3*(1/2-1/5+1/5-1/8+....+1/20-1/23)
=1/3*(1/2-1/23)
=1/3*21/46
=7/46
答
是不是题目出错了 如果是把“1/(3*5)+”换成“1/(5*8)+”就对了2,5,8,11,14,17,20,23..顺序增加31/(2*5)+1/(5*8)+1/(8*11)+...+1/(20*23)＝(1/3)*(1/2-1/5+1/5-1/8+1/8-1/11+.+1/20-1/23)=(1/3)*(1/2-1/23)=7/46...