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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Divergent series question

**Physics Forums | Science Articles, Homework Help, Discussion**