简算题:(1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)×128

  • 时间:2020-06-05 20:30:28
  • 分类:数学世界
  • 阅读:145 次

简算题:(1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)×128

数学题解答:把括号中每个加数,提取1/4,

得到:(1/2+1/6+1/12+1/20+……+1/72)×1/4×128

括号里面的你会算吗?1/2=1 – 1/2,1/6=1/2 – 1/3,1/12= 1/3 – /1/4,……

原式=(1/2+1/6+1/12+1/20+……+1/72) × 1/4 × 128

=(1 – 1/2 + 1/2 – 1/3 +1/3 – ……- 1/8 + 1/8- 1/9) × 1/4 × 128

=8/9 × 32

=256/9

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