$$x_{n+1}=\sqrt {\frac{1}{2} ( 1+x_n)}$$
Evaluate the limit $\mathscr{L}=\lim \limits_{n \rightarrow +\infty} \cos \left ( \frac{\sqrt{1-\xi^2}}{\prod \limits_{k=1}^{n} x_k} \right )$.
It's not necessary! Obviously assuming that $x_1\stackrel{(*)}{>}-1$, in any case the sequence $\{x_n\}_{n=1}^{\infty}$ is monotonic and bounded.dr.tasos wrote:I think you need to give an initial value though.
The above note comes after an interchange of private messages. Let's make it more clear:Tolaso J Kos wrote:...I am unable to check for any particular typos that may have occured during typesetting...
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