1/2-1/6-1/12-1/20-...-1/110

来源：学生作业帮助网编辑：六六作业网时间：2024/05/13 22:31:30

1/2-1/6-1/12-1/20-...-1/1101/2-1/6-1/12-1/20-...-1/1101/2-1/6-1/12-1/20-...-1/1101/111/111/2-1/6-1/1

1/2-1/6-1/12-1/20-...-1/110
1/2-1/6-1/12-1/20-...-1/110

1/2-1/6-1/12-1/20-...-1/110
1/11

1/11

1/2-1/6-1/12-1/20-...-1/110
=1/2-(3-2)/(2*3)-(4-3)/(3*4)-(5-4)/(4*5)-...-(11-10)/(10*11)
=1/2-[3/(2*3)-2/(2*3)]-[(4/(3*4)-3/(3*4)]-[(5/(4*5)-4/(4*5)]-...-[(11/(10*11)-10/(10*11)]
=1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-...-(1/10-1/11)
=1/2-1/2+1/3-1/3+1/4-1/4+1/5)-...-1/10+1/11
=1/11