Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

is the series ..

$$ \sum _{n=2}^{\infty}n^{kin} $$

here k is a real number

is convergen or divergent ??, for example perhaps we can copare it to the series $$ \sum _{n=2}^{\infty}n^{ix} $$ which is divergent for every fixed 'x'

what criterion could i use to check the convergence or divergence of the series ??

this series is related to the fourier series $$ \sum_{n=2}^{\infty}cos(xnln(n)) $$

share|improve this question
    
Does the general term tend to $0$? –  1015 Feb 12 '13 at 22:23
    
don't know.. i would have for big N the term $ \infty ^{i \infty} $ which makes no sense –  Jose Garcia Feb 12 '13 at 22:29
add comment

1 Answer

Hint: $$ |n^{ikn}|=|e^{ikn\ln n}|=1 $$ for all $n$. Do you know a criterion that could help now?

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.