Is there any formula for this
1^n +2^n +3^n +...+x^n

Question

Is there any formula for this
1^n +2^n +3^n +...+x^n

mathslover · Answer

why don't you try for a derivation ?

amoodarya · Answer

yes but is very complicated !

look these 
1+2+3 + ...n=n(n+1)/2
1^2+2^2 +...n^2=n(n+1)(2n+1)/6
1^3+2^3+...+n^3=(n(n+1)/2)^2

anonymous · Answer

no standard formula

anonymous · Answer

Cant it be expressed interms of x and n

amoodarya · Answer

its not easy to write when n is >4
but look
1+2+3+ ...+x=x(x+1)/2
is that "what you mean "?

shubhamsrg · Answer

Well these is no standard formula, you can only derive that formula for summation(i^n) if you know the value of summation(i^ (n-1)) which will require knowledge of summation(i^(n-2)) and so on.. :|

terenzreignz · Answer

This reminds me of a p-series...
$$\large \sum_{k=1}^{x}\frac{1}{k^{p}}$$
And then just set p = -n...
But we don't have such an expression for the x'th partial sum as far as I know, for any p-series

terenzreignz · Answer

Well, except for the ones @amoodarya mentioned, anyway.