Suppose that a sequence $y_n$ is defined iteratively by $y_0 = 1$ and $$ y_{ n + 1 } = \frac{ 1 }{ 2 + y_n } $$ Show that $\{ y_n \}_{ n \geq 0 }$ is a convergent sequence.
I'm not really sure where to start.
Suppose that a sequence $y_n$ is defined iteratively by $y_0 = 1$ and $$ y_{ n + 1 } = \frac{ 1 }{ 2 + y_n } $$ Show that $\{ y_n \}_{ n \geq 0 }$ is a convergent sequence.
I'm not really sure where to start.