${\sum }_{k=1}^n{k}^m$‚ÌŒöŽ®

• ${\displaystyle \sum _{k=1}^{n}k=\frac{n\left(n+1\right)}{2}}$�@�Ë“±�o
• ${\displaystyle \sum _{k=1}^n{k}^2=1^2+2^2+3^2\cdots +n^2}$${\displaystyle =\frac{n\left(n+1\right)\left(2n+1\right)}{6}}$�@�Ë“±�o
• ${\displaystyle \sum _{k=1}^n{k}^3=1^3+2^3+3^3+\cdots +n^3}$${\displaystyle ={\left\{\frac{n\left(n+1\right)}{2}\right\}}^2}$�@�Ë“±�o
• ${\displaystyle {\displaystyle \sum _{k=1}^n{k}^4}=1^4+2^4+3^4+\cdots +n^4}$${\displaystyle =\frac{1}{30}n\left(n+1\right)\left(2n+1\right)\left(3n^2+3n-1\right)}$�@�Ë“±�o

 

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