1~4幂次方和
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  • 楼主__KevinMZ__
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  • 发布时间2024/8/14 12:43
  • 上次更新2024/8/14 14:46:31
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1~4幂次方和
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__KevinMZ__楼主2024/8/14 12:43
∑i=1ni0=n∑i=1ni1=n(n+1)2∑i=1ni2=n(n+1)(2n+1)6∑i=1ni3=(n(n+1)2)2∑i=1ni4=n(n+1)(2n+1)(3n2+3n−1)30\sum_{i = 1}^n i^0 = n \\ \sum_{i = 1}^n i^1 = \frac{n(n + 1)}{2} \\ \sum_{i = 1}^n i^2 = \frac{n(n + 1)(2n + 1)}{6} \\ \sum_{i = 1}^n i^3 = (\frac{n(n + 1)}{2})^2 \\ \sum_{i = 1}^n i^4 = \frac{n(n + 1)(2n + 1)(3n^2 + 3n - 1)}{30}
2024/8/14 12:43
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