(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x) = (3 sin(x))/(2 + cos(x))

let x_0 be a number in (0, (2/3)*pi], and define a sequence recursively by setting

x_n+1 = f(x_n)

(1) prove that the sequence {x_n} is strictly decreasing sequence in (0, (2/3)*pi] and that lim x_n =0

(2) Find an integer k greater or equal to 1 such at {n^(1/k) x_n} is convergent to a finite, non-zero real number and evaluate lim n^(1/k) x_n

2. Relevant equations

3. The attempt at a solution

I tried the first problem by induction but I don't know how to prove it for P(n+1) (assuming P(n) is true). Any help is appreciated thank you.

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# Homework Help: Strictly decreasing sequence (analysis)

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