Convergent Real Sequence/Examples

Example: $x_{n + 1} = \dfrac k {1 + x_n}$
=== Example: $x_n = \sqrt {x_{n - 1} y_{n - 1} }$, $\dfrac 1 {y_n} = \dfrac 1 2 \paren {\dfrac 1 {x_n} + \dfrac 1 {y_{n - 1} } }$ ===