Originally Posted by

**IrrationalPI3** Hey everyone i was doing some AP work on my own and couldnt figure out how to do this question with induction. i know the steps just cant figure out how to use it in this case. Any help would be appreciated

$\displaystyle

a_n = \sqrt{2 +\sqrt {2+ \sqrt{2+\cdots + \sqrt2}}}

$

"n roots"

not sure if i typed it properly, but all of the square roots are under the first one so its the square root of (2 + squareroot of 2 + squareroot of 2) "n" times...

then i have to:

use induction to prove the sequence is increasing

and prove if its bounded above by 2

thanks in advance