Sums of Integer Powers - C(s) Convergence

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SUMMARY

The discussion centers on the closed form expression for the convergence of the series C(s) = ∑_{n=1}^{N} n^{s}. For fixed N and integer s, closed form solutions exist, although they become complex for larger values of s. It is established that C_N(s) will be a polynomial in N of degree s+1. This topic has been previously addressed in another thread on the general math forum.

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adoado
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Hello all,

Is there a closed form expression for the convergence of

[tex]C(s) = \sum_{n=1}^{N} n^{s}[/tex]

Cheers,
Adrian
 
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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 CN(s) will be a polynomial in N of degree s+1.
 

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