Study the following sequence

Asked Sep 16 '20 at 10:20

Active Sep 16 '20 at 10:29

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I am having trouble studying the following sequence $(x_k)_{k \geq 2}$ :

$$x_2= 2, \quad x_{k+1}= \frac{x_k}{\cos{(\pi 2^{-k})}}$$

I want to show that this sequences converges to $\pi$, but I have honestly no idea where to start.

Thanks for your help.

edited Sep 16 '20 at 10:29

asked Sep 16 '20 at 10:20

Velobos

1

Maybe this can help https://math.stackexchange.com/q/455995/399263 – zwim Sep 16 '20 at 10:26
Thank you ! It is exactly what i needed. – Velobos Sep 16 '20 at 10:43
2

Voting to close as answered in the link found by @zwim. – metamorphy Oct 02 '20 at 10:32

0 Answers0