这道题怎样做:1/﹙1×5﹚+1/﹙5×9﹚+1/﹙9×13﹚……+1/﹙97+101﹚
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/29 19:37:02
这道题怎样做:1/﹙1×5﹚+1/﹙5×9﹚+1/﹙9×13﹚……+1/﹙97+101﹚
![这道题怎样做:1/﹙1×5﹚+1/﹙5×9﹚+1/﹙9×13﹚……+1/﹙97+101﹚](/uploads/image/z/19529087-23-7.jpg?t=%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E6%A0%B7%E5%81%9A%EF%BC%9A1%2F%EF%B9%991%C3%975%EF%B9%9A%EF%BC%8B1%2F%EF%B9%995%C3%979%EF%B9%9A%EF%BC%8B1%2F%EF%B9%999%C3%9713%EF%B9%9A%E2%80%A6%E2%80%A6%EF%BC%8B1%2F%EF%B9%9997%EF%BC%8B101%EF%B9%9A)
原式可写为
4[(1-1/5)+(1/5-1/9)+(1/9-1/13)+……+(1/97-1/101)]
=4(1-1/5+1/5-1/9+1/9-1/13+……+1/97-1/101)
=4(1-1/101)
=4*100/101
=400/101
4[(1-1/5)+(1/5-1/9)+(1/9-1/13)+……+(1/97-1/101)]
=4(1-1/5+1/5-1/9+1/9-1/13+……+1/97-1/101)
=4(1-1/101)
=4*100/101
=400/101