Q:

Mathematical function that converges towards $7$?

My friends and I are finishing High School in Denmark. We have to do a math poster for some school activity, where the poster needs to have something to do with the number $7$. So my question is: does someone know a cool mathematical function that converges towards $7$? 
We covered Calculus III, so we should be able to understand a little math!

A:

One with the Fibonacci sequence:
$$
\lim_{n\to\infty}\frac{4F_{n+1}^2 - 4F_{n+1}F_n + 3F_n^2}{F_n^2} =
\lim_{n\to\infty}\left(2\frac{F_{n+1}}{F_n} - 1\right)^2 + 2 = 
7.
$$

A:

If integrals are acceptable, this one is nice:
$$
7= \frac{1}{\displaystyle\int_0^1 \frac{x^4(1-x)^4}{1+x^2} \, dx +\pi-3}
$$
(source: Wikipedia)

A:

Here is one that looks crazy at first, but it is actually quite simple:
$$\lim\limits_{N\to\infty}\left[\frac N{3\pi}\sin\left(\frac{42}{N}\sum\limits_{k=1}^N\left(\frac{\pi}{\pi+2}\right)^k\right)\right] = 7. $$

