How to find the limit of the sequence defined by $x_{n+1}=\sqrt{4 x_n -3}\,$?
Solution 1:
Note that if $x_n \gt 3, x_{n+1} \gt 3$ so your entire sequence is bounded below by $3$.
Note that if $x_n \gt 3, x_{n+1} \gt 3$ so your entire sequence is bounded below by $3$.