anonimnystefy

well the object you posted is the Deltoid curve.it has a Wiki page:Deltoid curve ,but i'm not sure what you want with it.

What I always did with these kind of problems is take that xk is equal to xk+n or xk-n when k goes to infinity,and n doesn't. if xk is equal to some x as x goes to k,than from your equation we get: [math]x=\frac{2}{x+x}[/math] [math] x=\frac{1}{x}[/math] [math]x^2=1[/math] [math]x=1[/math] you can also use the Ratio test which states that [math]x_n[/math] converes if [math]\lim_{n\to \infty}\ \frac{x_{n+1}}{x_n}<1[/math]