\[\sum_{}^{} {n^s} = ?\]

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\[0^0\] \[0!\] \[x! (x<0)\]

\[(a+b)^n = \frac{n!}{(n-k)!k!}a^{n-k}b^k\] \[\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{{\pi}^{2}}{6}\] \[\sum_{n=1}^{k} {a^n} = \frac{{a^{k+1}-1}}{a-1}\] \[\sum_{n=a}^{b} {n} = \frac{(a+b)(b-a+1)}{2}\] \[\sum_{n=a}^{b} {n^2} = \frac{(a-b)(2b^2 + 2ab + 3b +2a^2 + 3a +1)}{6}\] \[\sum_{n=a}^{b} {n^2} = \frac{(a-b)(2b^2 + 2ab + 3b +2a^2 + 3a +1)}{6}\]