# Math Help - infinite sequences

1. ## infinite sequences

heyy everyone.
I was having some trouble doing an assignment for math so i hope u guys can help me.
I have to find a formula for an+1 in terms of an for this infinite sequence:

a1 = square root of 1 + sqaure root of 1
a2 = square root of 1 + square root of 1 + square root of 1
a3 = squareroot of 1 + squareroot of 1 + squareroot of 1 + squareroot of 1
....etc (its infinite)

help plzz!
thx
=]

2. Helo, 'kaleyy =]!

I assume those are "nested" square roots.
Otherwise, it makes no sense.

I have to find a formula for $a_{n+1}$ in terms of $a_n$ for this infinite sequence:

$a_1\:=\:\sqrt{1 + \sqrt{1}}$

$a_2 \:=\:\sqrt{1 + \underbrace{\sqrt{1 + \sqrt{1}}}_{\text{This is }a_1} }$

$a_3 \:=\:\sqrt{1 + \underbrace{\sqrt{1 + \sqrt{1 + \sqrt{1}}}}_{\text{This is }a_2}}\quad\hdots$ etc.

. . $a_{n+1} \;=\;\sqrt{1 + a_n}$

3. ohhh that makes so much sense.
lol i looked at the all the square roots and i panicked.
=D
thx soo much.
btw they were ""nested"" square roots.

4. ok so if i had to do this same problem but i had to use 2 instead of 1 my a(n+1) wld be:
squareroot(2 + an)

right?