# Math Help - Value of a continued fraction.

1. ## Value of a continued fraction.

THe following is called a continued fraction. It equal an irrational number. Find that number.
It is basically
2 plus half+ half of half + half of half of half.....
It just keep on going
i really need your help

2. Originally Posted by vvc531
THe following is called a continued fraction. It equal an irrational number. Find that number.
It is basically
2 plus half+ half of half + half of half of half.....
It just keep on going
i really need your help
$U(n) = 2+(\frac{1}{2})^n$

We can treat the right hand side as a geometric sequence:

$a = \frac{1}{2} , r = \frac{1}{2}$ n = infinity

$S(infinity) = \frac{a}{1-r} = \frac{0.5}{1-0.5} = 1$

this means the sum of the infinite terms is 1 and adding this to the existing 2 we get a limit of 3