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.

Using Mathematica I found that the relation $$\sum_{k=1}^n\left(\left(\frac{3}{2}\right)^k\ (\mathrm{mod}\ 1)\right)\approx\frac{n}{2}$$ seems to hold. Actually, every fraction of the form $\frac{b}{a}$, with $b>a$ and $\mathrm{gcd}(a,b)=1$, seems to behave similarly. Example, $\frac{3}{2}$:

graph

So, can we prove some asymptotic formula or somehow show that this behavior is constant?

share|improve this question
add comment

1 Answer

up vote 0 down vote accepted

You might be interested in this: http://mathworld.wolfram.com/PowerFractionalParts.html

share|improve this answer
    
Ooh, I am. Thanks! –  Carolus Jul 3 '12 at 10:16
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.