Perhaps an easy an interesting thing to do is to solve an equation looking for a fixed point. For example to solve x=x^2 if you iterate x_(n+1)=x_n^2 then you o

Perhaps an easy an interesting thing to do is to solve an equation looking for a fixed point. For example to solve x=x^2 if you iterate x_(n+1)=x_n^2 then you obtain the solution 0 (in case your initial x is between -1 and 1), then you thing about looking for x = sqrt(x) and discover that it converges to 1 if you choose x1 > 1. This is simple and make you thing a little the power of iterating for solving certain types of problems like equations.