数列求和之四——错位相减求和

  • 时间:2020-04-06 17:43:36
  • 分类:数学世界
  • 阅读:103 次

这种求和方式较为少见,平时数学学习习中较少用到,但它确实非常巧妙。这里用到了一个方法,叫做构造2S,因为先把原来的数列整体看作为字母S,那么2S减去S正好仍然等于原来的数列。由于2S与S这两个数列中有重叠的部分,所以在相减的过程中重叠的部分全部消去,只剩下2S中的最后一个数减S中的第一个数,这样就非常方便地算出了得数,可以说巧妙至极。

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