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 October 30th, 2017, 03:05 AM #1 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित proof given: $\displaystyle n\geq 1$, $\displaystyle a > 0$, $\displaystyle x_{1} >0$ $\displaystyle x_{n+1} = \frac {1}{2}(x_{n} + \frac{a}{x_{n}})$ to prove: a. $\displaystyle x_{n} \geq \sqrt {a}$ for all $\displaystyle n \geq 2$ b. $\displaystyle x_{n+1} \leq x_{n}$ for all $\displaystyle n \geq 2$ and deduce $\displaystyle x_{n}$ is convergent c. find $\displaystyle \lim_{n \to \infty} x_{n}$ how should I begin? sorry if I posted this in wrong section.
 October 30th, 2017, 05:51 PM #2 Member   Joined: Jan 2016 From: Athens, OH Posts: 89 Thanks: 47 I think this should go in the calculus section. Here is most of a solution; I've left a few details for you. Thanks from topsquark and MATHEMATICIAN

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