could some one help please
let a1=2
an+1=3+an^2/2an
prove n>=1 an>root3
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!