计算:2/3*5+1/5*7+1/7*9+1/9*11+1/11*13

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 17:43:38
计算:2/3*5+1/5*7+1/7*9+1/9*11+1/11*13

计算:2/3*5+1/5*7+1/7*9+1/9*11+1/11*13
计算:2/3*5+1/5*7+1/7*9+1/9*11+1/11*13

计算:2/3*5+1/5*7+1/7*9+1/9*11+1/11*13
2/3*5+1/5*7+1/7*9+1/9*11+1/11*13
=1/15+1/2(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)
=1/15+1/2(1/3-1/13)
=38/195

2/3×5+1/5×7+1/7×9+1/9×11+1/11×13
=2/15+1/2×﹙1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13﹚
=2/15+1/2×﹙1/5-1/13﹚
=2/15+4/65
=38/195.

原式=1/2(1/3-1/5+1/5-1/7+...+1/11-1/13)
=1/2(1/3-1/13)
=5/39