Hi everyone,

This is my first post here some i'm little worried : will i do someting wrong ? We'll see x)

That's because i'm french, and even if my english is not very very bad, i'm likely to make sometimes some mistakes. So, forgive me about that :')

I'm not quite sure i post in the right forum too. Well, i don't even get how the American education system works (pre-university, university, and all that...)

Anyway, i choose this forum 'cause it seems to be pretty serious, and that's exactly what i was looking for as student in mathematics, a place where i can help people and where people can help me too

Anyway, i dared to begin this post, this is for a reason. I just can't get over an exercice our teacher gave us.

Well, the first part of this exercice was about a sequence which was defined by :

$\displaystyle u_n = \prod_{k=1}^{n} \cos \frac{\theta}{2^k}$

with $\displaystyle \theta \in ]-\pi ; \pi]$

I (if i am not wrong) had to study it and found that $\displaystyle \lim_{n \to + \infty} u_n = 1$

Well, after that, there's another question which looks like this :

Let $\displaystyle \forall x \geq 0, z_{n+1} = \frac{z_n+|z_n|}{2}$

Determine the limit of $\displaystyle \left ( z_n \right )_{n\geq 0 }$ which depends of $\displaystyle z_0$.

And, i just can't see how this question is related to the previous one (because they must be connected in some way !). I've already find that

$\displaystyle \forall n \geq 1, |z_{n+1}| \leq |z_n|$

I, of course, don't want the answer, but just some tips which could help me in some way

Thanks for taking your time to read me,

Hugal.