1 / (5x7) +1 / (7x9) +1 / (9x11)+ 1 / (11x13)+ 1 / (13x15)不能只有答案,

来源：学生作业帮助网编辑：作业帮时间：2024/11/15 14:10:35

1 / (5x7) +1 / (7x9) +1 / (9x11)+ 1 / (11x13)+ 1 / (13x15)不能只有答案,
1 / (5x7) +1 / (7x9) +1 / (9x11)+ 1 / (11x13)+ 1 / (13x15)
不能只有答案,

1 / (5x7) +1 / (7x9) +1 / (9x11)+ 1 / (11x13)+ 1 / (13x15)不能只有答案,
1 / (5x7) +1 / (7x9) +1 / (9x11)+ 1 / (11x13)+ 1 / (13x15)
=1/2×(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2×(1/5-1/15)
=1/15

1 / (5x7) +1 / (7x9) +1 / (9x11)+ 1 / (11x13)+ 1 / (13x15)
=1/2x(1/5-1/7)+....+1/2x(1/13-1/15)
=1/2x(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2x(15-1/15)
=1/15

原式=1/2*(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)=1/2*(1/5-1/15)=1/15