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.

Can someone help me prove that the limit approaches zero, I know it does, but I can't prove it.

$$\lim_{n\to\infty} \sum\limits_{k=1}^n \frac{\ln k}{n} \left( 1-\left\{\frac{n}{k} \right\} \right) \left( \left(1-\frac{k}{n} \left\{\frac{n}{k}\right\} \right)-\frac{1}{2} \right)$$

where $\displaystyle \left\{ \frac{n}{k} \right\}$ is the fractional part of $\displaystyle \frac{n}{k}$.

share|improve this question
1  
Please consider adding $\LaTeX$ format to your question –  Pragabhava Oct 26 '12 at 2:24
    
how do i do that –  boby Oct 26 '12 at 2:26
    
@boby I typeset your fomulae using $\LaTeX$, please check if my interpretation is correct. Also to other members, is there a better notation for the Fractional function? –  FrenzY DT. Oct 26 '12 at 2:28
    
Thanks a bunch, could you help me prove it though? I tested it on wolfram alpha and it aproaches zero quite fast but I still cant prove it –  boby Oct 26 '12 at 2:29
1  
To answer your question "how do i do that": meta.math.stackexchange.com/questions/107/… –  joriki Oct 26 '12 at 4:18
show 5 more comments

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.