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.

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