Question

Find the value of x:
\[x = \frac{1}{1 + \frac{1}{1+ \frac{1}{1 + ...}}}\]

Answer 1

do we do x = 1/(1+x)?

Answer 2

\[ x = \frac{1}{1 + x} \] and then ...

Answer 3

so
x*(x+1)=1
x^2 +x -1=0

Answer 4

x1 = (-1-sqrt(5))/2
x2 = (-1+sqrt(5))/2

Answer 5

wait it's x2 right?

Answer 6

yeah it can never be negative

Answer 7

lol yea.. i just noticed haha

Answer 8

hey this that one question that is troubling me for llife.
Can any one explain how to solve these types of question

Answer 9

refer to this its the same concept: nested fractions and nested radicals
http://openstudy.com/study#/updates/4f391d36e4b0fc0c1a0df88b