Sums of Integer Powers - C(s) Convergence

[adoado]

Hello all,

Is there a closed form expression for the convergence of

$$C(s) = \sum_{n=1}^{N} n^{s}$$

Cheers,
Adrian

 

[mathman]

What do mean by convergence? For fixed N and integer s, there are closed form solutions, although things get messy looking for larger s. In general C_N(s) will be a polynomial in N of degree s+1.

 

[Mute]

This was asked in another thread in the general math forum a couple weeks ago:

https://www.physicsforums.com/showthread.php?t=469498