Plus And Minus

Calculus Level 2

$1 + \dfrac1{1 + \dfrac1{1 + \dfrac1{1 + \ddots }}}$

The value of the infintely nested fraction above is equal to $\dfrac{1+\sqrt5}2$ . Find the value of the infinitely nested fraction below.

$1 - \dfrac1{1 - \dfrac1{1 - \dfrac1{1 - \ddots }}}$

Give your answer to 3 decimal places.

If you think that this number is a finite non-real number, submit your answer as 12345.

If you think that this number that does not converge (doesn't exist), submit your answer as 67890.