Nested

Algebra Level 3

What is the value of $\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+_\ddots}}} ?$

1 solution

Rajdeep Ghosh
May 19, 2017

Let $\frac{1}{1+\frac{1}{1+\frac{1}{1+...}}}=x$

or, $\frac{1}{1+x}=x$

or, $x(x+1)=1$

or, $x^2+x-1=0$

Applying the quadratic formula, $\frac{1}{1+\frac{1}{1+\frac{1}{1+...}}}=0.618033$

I just kept wondering what am I doing wrong.. Turns out I did something wrong in ABC... Didn't use - 1...

Peter van der Linden - 4 years ago

not an issue. all of us do that all the time.

Rajdeep Ghosh - 4 years ago

Hehe but it gives you the feeling like: huh I can do this, I know, but why don't I get the right answer?

Peter van der Linden - 4 years ago