# Thread: Help involving induction proof

1. ## Help involving induction proof

Hi, I'm having a lot of trouble with the following problem:

let $\displaystyle a_1 = 2$ and $\displaystyle a__(n+1)$ $\displaystyle = \frac{4a_(n-1) - 3} {a_n} for n \geq 1.$ Show that $\displaystyle 1 \leq a_n \leq a_(n+1) \leq 3$ for all $\displaystyle n \geq 1$

I am very confused about how to actually show that the above statement is true in the form of a proof, and would greatly appreciate any help.

2. Originally Posted by spoc21
Hi, I'm having a lot of trouble with the following problem:

let $\displaystyle a_1 = 2$ and $\displaystyle a__(n+1)$ $\displaystyle = \frac{4a_(n-1) - 3} {a_n} for n \geq 1.$ Show that $\displaystyle 1 \leq a_n \leq a_(n+1) \leq 3$ for all $\displaystyle n \geq 1$

I am very confused about how to actually show that the above statement is true in the form of a proof, and would greatly appreciate any help.
I think you have to say what $\displaystyle a_0$ is...

Also, finding $\displaystyle \displaystyle \lim_{n \to \infty}a_n = \lim_{n \to \infty}a_{n - 1} = \lim_{n \to \infty}a_{n+1}$ would be a good place to start.