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## Homework Statement

The sequence of positive numbers ##u_1,u_2,u_3...## is such that ##u_1<4## and ##u_{n+1}= \frac{5u_n+4}{u_n+2} ##

i. By considering ##4-u_{n+1} ##, prove by induction that ##u_1<4## for ##n\geq 1##

Mod note: The above is incorrect. In a later post the OP revised this to

Faiq said:i. By considering ##4−u_{n+1}##, prove by induction that ##u_n<4## for all ##n\geq1##

## The Attempt at a Solution

I have never been introduced to these types of backward induction so I am not aware of the statements I have to make and prove. I do get the general idea that it's like finding the limit of ##4-u_{n+1} ## as ##u_n \rightarrow 4## and then say that since as the upper limit of the function is 0, then it must be smaller than 0. So it would be very helpful if I am given an outline on how to solve this.

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