Proving inf(x_n)=1 for x_{n+1}=2-\frac{1}{x_n}

[hockey777]

x_{n+1}=2-\frac{1}{x_n}

I need to show that inf(x_n)=1

For someone reason this is proving to be more difficult than I thought, could someone pleas help?

 

[mathman]

It would be a little clearer if you defined x_0. Also your notation is a little strange - frac{1}{x} means what? I am guessing it means the fractional part, but I am not sure.

 

[tiny-tim]

Welcome to PF!

$$x_{n+1}=2-\frac{1}{x_n}$$

I need to show that inf(x_n)=1

Hi hockey777! Welcome to PF!

Hint: start by subtracting 1 from each side.

(and type [noparse]$$before and$$ after your equations![/noparse] )