- #1

riskandar

- 3

- 0

## Homework Statement

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

## Homework Equations

## 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.