累乗の和

$$\sum_{k=1}^{n}k=\frac{1}{2}n(n+1)$$ (1.9)

$$\sum_{k=1}^{n}k^2=\frac{1}{6}n(n+1)(2n+1)$$ (1.10)

$$\sum_{k=1}^{n}k^3=\frac{1}{4}n^2(n+1)^2=\left\{\frac{1}{2}n(n+1)\right\}^2$$ (1.11)