Help involving induction proof

**spoc21** · October 3rd 2010, 07:04 PM

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

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

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.

**Jhevon** · October 3rd 2010, 07:47 PM

Originally Posted by spoc21

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

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

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 $a_0$ is...

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

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