could some one help please

let a1=2

an+1=3+an^2/2an

prove n>=1 an>root3

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- Feb 5th 2010, 11:49 AMrussell2010Induction for an inequality
could some one help please

let a1=2

an+1=3+an^2/2an

prove n>=1 an>root3 - Feb 5th 2010, 10:51 PMbmp05
hmmm... this is an interesting question, but I'm not sure if I've understood it correctly. Do you mean:

$\displaystyle

a_{n + 1} = (\frac{3 + a_n^2}{2a_n}) $; $\displaystyle n > 1, a_n > \sqrt{3}

$ ?

Oops, took me a while to figure out what was meant by the question...

$\displaystyle

a_{n + 1} = \frac{3 + (\sqrt{3})^2}{2(\sqrt{3})} = \frac{3}{\sqrt{3}} =\sqrt{3}$ ; substitue $\displaystyle a_n = \sqrt{3}$

mind you that's not an answer!