What Are the Properties of the Sequence (Xn)?

[l888l888l888]

Homework Statement

let (Xn) be a sequence in R given by X1=1 and Xn+1=1/(3+Xn) for n>=2. prove Xn converges and find the limit.

Homework Equations

The Attempt at a Solution

well i think using the monotone convergence theorem would help but i would have to prove that the sequence is bounded and monotone. But I have not been able to prove it is monotone yet.

 

[SammyS]

Show us your work so we can help you.

Sometimes it helps to generate the first few terms of a sequence.

 

[l888l888l888]

X2=1/4, X3=4/13, X4=13/43, X5=43/142... the sequence kinda flips up and down. it will go down, up, down,... it does not seem monotone...

 

[SammyS]

How is x_n+2 related to x_n ?

Then look at the subsequences, (x_2n) and (x_2n+1).