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Question Number 9232 by geovane10math last updated on 24/Nov/16

1 + 2 + 3 + 4 +...+ n = ((n(n + 1))/2)  1^2 +2^2  +3^2  +...+ n^2  = ((n(n+1)(2n+1))/6)  1^x  + 2^x  + 3^x  +...+ = n^x  = Formula?  x ∈ R

$$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+...+\:{n}\:=\:\frac{{n}\left({n}\:+\:\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} \:+\mathrm{3}^{\mathrm{2}} \:+...+\:{n}^{\mathrm{2}} \:=\:\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$$$\mathrm{1}^{{x}} \:+\:\mathrm{2}^{{x}} \:+\:\mathrm{3}^{{x}} \:+...+\:=\:{n}^{{x}} \:=\:\mathrm{Formula}? \\ $$$${x}\:\in\:\mathbb{R} \\ $$

Commented by sou1618 last updated on 25/Nov/16

Commented by sou1618 last updated on 25/Nov/16

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