let be the divergent series:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]1^p+2^p+3^p+.....................+N^p=S(N) [/tex] with p>0 my

question is..how i would prove that this series S would diverge in the form:

[tex]S(N)=N^{p+1}/p+1 [/tex] N--->oo

for the cases P=1,2,3,... i can use their exact sum to prove it but for the general case i can not find any prove..perhaps i should try Euler sum formula ..are the divergent series S(N) equal to the integral:

[tex]\int_{0}^{\infty}dxx^{p} [/tex] they both diverge in the same way.

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# Divergent series question

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