Formulas of the sums of a number of natural numbers in integer degree

$1+2+3+4+5+....+(n-1)+n=\frac{n(n+1)}{2}$

This is a well-known formula, discovered by Gauss at the age of six.

### The sum of the natural series where each element is raised to the second degree

$1^2+2^2+3^2+4^2+5^2+....+(n-1)^2+n^2=\frac{1}{6}(2n^3+3n^2+n)$

### $1^{12}+2^{12}+3^{12}+4^{12}+5^{12}+....+(n-1)^{12}+n^{12}=\frac{1}{2730}(210n^{13}+1365n^{12}+2730n^{11}-5005n^9+8580n^7-9009n^5+4550n^3-691n)$

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