# Induction for an inequality

• Feb 5th 2010, 11:49 AM
russell2010
Induction for an inequality
let a1=2

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

prove n>=1 an>root3
• Feb 5th 2010, 10:51 PM
bmp05
hmmm... this is an interesting question, but I'm not sure if I've understood it correctly. Do you mean:
$
a_{n + 1} = (\frac{3 + a_n^2}{2a_n})$
; $n > 1, a_n > \sqrt{3}
$
?

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

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

mind you that's not an answer!