# Proof involving linear algebra (1 Viewer)

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#### spoc21

1. The problem statement, all variables and given/known data
Hi, I'm supposed to solve the following question using proof by induction, and am very confused with it. It would be greatly appreciated if someone could help me solve this problem:

Let an = 2 and an+1$$\frac{4a_n -3}{a_n}$$ for n >=1. Show that 1$$\leq a_n \leq a_(n+1)\leq3$$ for all n $$\geq1$$
please note that _ = subscript

I am very confused with this problem, and would appreciate any help.

Thanks!

#### JThompson

What you posted doesn't make sense. Check to make sure that it's written correctly.

#### Susanne217

1. The problem statement, all variables and given/known data
Hi, I'm supposed to solve the following question using proof by induction, and am very confused with it. It would be greatly appreciated if someone could help me solve this problem:

Let an = 2 and an+1$$\frac{4a_n -3}{a_n}$$ for n >=1. Show that 1$$\leq a_n \leq a_(n+1)\leq3$$ for all n $$\geq1$$
please note that _ = subscript

I am very confused with this problem, and would appreciate any help.

Thanks!
I have myself solved something simular not so long a ago I think it suppose to say

Let $$a_n = 2$$

Let $$a_{n+1} = \frac{4 {a_n}-3}{a_n}$$ for $$n \geq 1$$

and then

"Show that 1$$\leq {a_n} \leq {a_{n+1}}\leq 3$$ for all $$n \geq 1$$"

I could be wrong but this setup makes me think about a socalled recurrence relation..
But you are right it looks like something is missing.

Last edited:

#### Gavins

Have you tried anything yet? Induction has some very clear steps. First, show it is true for n=1. Then assume n=k is true and see what happens with k+1.

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