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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

Consider the Recursive Sequence Defined By x1=1;xn+1=xn2+22xn,n>1x _ { 1 } = 1 ; x _ { n + 1 } = \frac { x _ { n } ^ { 2 } + 2 } { 2 x _ { n } } , n > 1x1​=1;xn+1​=2xn​xn2​+2​,n>1

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