lets-x-gt-0-and-take-the-sequence-a-a-0-x-a-n-1-x-a-n-i-proof-that-0-a-n-a-n-1-ii-proof-that-M-such-that-a-n-M-iii-using-i-and-ii-proof-that-lim-n-a-n-exist-iv-compute-lim-n

Question Number 1635 by 123456 last updated on 28/Aug/15

lets x > 0, and take the sequence a

a_{0} = \sqrt{x}

a_{n + 1} = \sqrt{x + a_{n}}

i . proof that 0 ⩽ a_{n} ⩽ a_{n + 1}

ii . proof that \exists M such that a_{n} ⩽ M

iii . using i and ii proof that \lim_{n \to \infty} a_{n} exist

iv . compute \lim_{n \to \infty} a_{n}