作业帮1/2+1/6+1/12+1/20+1/30+1/42+1/56 ; 1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 19:29:50
1/2+1/6+1/12+1/20+1/30+1/42+1/56 ; 1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13
1/2+1/6+1/12+1/20+1/30+1/42+1/56 ; 1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13
1/2+1/6+1/12+1/20+1/30+1/42+1/56 ; 1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13
1/2+1/6+1/12+1/20+1/30+1/42+1/56 =1/(1*2)+1/(2*3)+1/(3*4)+.+1/(7*8) =1-1/2+1/2-1/3+1/3-1/4...+1/7-1/8 =1-1/8 =7/8 补充：1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13 =1/2*(1-1/3+1/3-1/5+1/5-1/7...+1/77-1/13) =1/2*(1-1/13) =1/2*12/13 =6/13