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October 30th, 2017, 04:05 AM   #1
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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.
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October 30th, 2017, 06:51 PM   #2
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I think this should go in the calculus section. Here is most of a solution; I've left a few details for you.

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