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Math Help - Help involving induction proof

  1. #1
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    Help involving induction proof

    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.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by spoc21 View Post
    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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