Sign up ×
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.

Possible Duplicate:
Self-Contained Proof that $\sum\limits_{n=1}^{\infty} \frac1{n^p}$ Converges for $p > 1$

We know that $\lim u_n=\sum_{i=1}^{n} \frac{1}{i} =\infty $. But I can't prove that with $\beta >1$: $u_n=\sum_{i=1}^{n} \frac{1}{i^\beta}$ converge

share|cite|improve this question

marked as duplicate by Marvis, Alexander Gruber, Ittay Weiss, Rahul, Austin Mohr Jan 7 '13 at 5:38

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Do you know the integral test? – Brian M. Scott Jan 7 '13 at 4:31
Here is a beautiful argument by joriki. – user17762 Jan 7 '13 at 4:31
thanks you so much – Haruboy15 Jan 7 '13 at 4:33

1 Answer 1

Hint: Let $U = u_{\infty}$. Think about the relationship between $iU$ and $U$.

share|cite|improve this answer
What is for you exactly $\,u_\infty\,$?? – DonAntonio Jan 7 '13 at 4:42

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