and ![$f:[a,b]\rightarrow\mathbb{R}$](http://latex.artofproblemsolving.com/6/7/c/67c320754a36aaec178e61f04bfcbac41c0bf675.png)
be a strictly monotonous function such that 
.
.
for which there exists a scrictly monotonous function 
such that 
be a prime number. A flea is staying at point 
of the real line. At each minute,
to the left or to the right.
minutes, it wants to be at 
the number of its strategies to do this
:
and 
are two positive sequences and
Prove that ![$$\lim_{n\to\infty}\frac1n\log\left[1+\left(\frac{b_n}{a_n}\right)^n\right]=0.$$](http://latex.artofproblemsolving.com/9/f/d/9fd7d054dfb137c6667b8fd0a05ad173213455ed.png)
I can prove it by 
method, I want to know if there is another method!
and 
,
.
Mathematical Gazette
that satisfies the functional equation
for all 
such that![\[\lim_{n \to \infty} \left( \frac{1 + 2^{1/3} + 3^{1/3} + \dots + n^{1/3}}{n^t} \right ) = c\]](http://latex.artofproblemsolving.com/e/1/a/e1a87bd7bee41a7d656e2ff067a87dff0c9929ec.png)
for some real 
.
.
be a continuous function such that for all 
and for all 
,
Show that 
is a constant function.
Y by
So I don't really care if I dox myself but I went to one of the single worst chapters in all of Florida, the Indian river chapter(even the runner of mathcounts states was sayin we would lose to osprey in states). I don't exactly know what my score is, but all I know is that I got 1st place sprint and chapter but then sold CD. If I had to guess, my score was around the 30-37 range. I also mocked at around a 70 on amc 10. My questions are:
1.
What are my chances of me getting nats qual
2.
Should I study the day before the competition
1.
What are my chances of me getting nats qual
2.
Should I study the day before the competition
