Consider the Recursive Sequence Defined By $x _ { 1 } = 1 ; x _ { n + 1 } = \frac { x _ { n } ^ { 2 } + 2 } { 2 x _ { n } } , n > 1$

Short Answer

Consider the recursive sequence defined by $x _ { 1 } = 1 ; x _ { n + 1 } = \frac { x _ { n } ^ { 2 } + 2 } { 2 x _ { n } } , n > 1$ . You may assume
the sequence to be monotonic (after the first term) and bounded and hence convergent. Find
its limit.