Proof involving linear algebra

[spoc21]

Homework Statement

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 a_n = 2 and a_n+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]

Homework Statement

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 a_n = 2 and a_n+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.

 

[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.