作业帮已知（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……用类似方法计算8/(3×3)+16/(15×15)+24/(35×35)+32/(63×63)+40/(99×99)+48/(143×143)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 17:05:26
已知（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……用类似方法计算8/(3×3)+16/(15×15)+24/(35×35)+32/(63×63)+40/(99×99)+48/(143×143)
已知（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……
（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……
用类似方法计算8/(3×3)+16/(15×15)+24/(35×35)+32/(63×63)+40/(99×99)+48/(143×143)
已知（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……（1/3-1/5）×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……用类似方法计算8/(3×3)+16/(15×15)+24/(35×35)+32/(63×63)+40/(99×99)+48/(143×143)
8/(3×3)+16/(15×15)+24/(35×35)+32/(63×63)+40/(99×99)+48/(143×143) =1/(1×1)-1/(3×3)+(1/(3×3)-1/(5×5))+(1/(5×5)-1/(7×7))+(1/(7×7)-1/(9×9))+(1/(9×9)-1/(11×11))+(1/(11×11)-1/(13×13))=1/(1×1)-1/(13×13))=168/169