题目

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)

提问时间：2021-03-13

答案

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