Evaluate 1-1/(1-1/(1-1/2))

$1 - \frac{1}{1 - \frac{1}{1 - \frac{1}{2}}}$

Simplify each term.

Simplify the denominator.

Write $1$ as a fraction with a common denominator.

$1 - \frac{1}{1 - \frac{1}{\frac{2}{2} - \frac{1}{2}}}$

Combine the numerators over the common denominator.

$1 - \frac{1}{1 - \frac{1}{\frac{2 - 1}{2}}}$

Subtract $1$ from $2$ .

$1 - \frac{1}{1 - \frac{1}{\frac{1}{2}}}$

Simplify the denominator.

Multiply the numerator by the reciprocal of the denominator.

$1 - \frac{1}{1 - (1 \cdot 2)}$

Multiply $2$ by $1$ .

$1 - \frac{1}{1 - 1 \cdot 2}$

Multiply $- 1$ by $2$ .

$1 - \frac{1}{1 - 2}$

Subtract $2$ from $1$ .

$1 - \frac{1}{- 1}$

Divide $1$ by $- 1$ .

$1 - - 1$

Multiply $- 1$ by $- 1$ .

$1 + 1$

Add $1$ and $1$ .

$2$