A new method for determining the limits of recursion relations

by ayushkhaitan3437

This is meant as a note. I will definitely expand this article later.

I hope this method has not been discovered before :(.

Say x_n=f(x_{n-1}) is a recursion relation. Then \lim\limits_{n\to\infty} x_n is the intersection point of y=f(x) and x=f(y).

For example, if we have x_n=\sqrt{5 x_{n-1}+6}, then \lim\limits_{n\to\infty} x_n is the y-coordinate of the intersection of y=\sqrt{5x+6} and x=\sqrt{6y+5}.