Solve 1/1-1{1-frac{1/1-frac{1{2018}}}}

$$\frac{ 1 }{ 1- \frac{ 1 }{ 1- \frac{ 1 }{ 1- \frac{ 1 }{ 2018 } } } }$$

Evaluate

$$\frac{1}{2018}\approx 0.00049554$$

Solution Steps

Convert 1 to fraction \frac{2018}{2018}.

$$\frac{1}{1-\frac{1}{1-\frac{1}{\frac{2018}{2018}-\frac{1}{2018}}}}$$

Since \frac{2018}{2018} and \frac{1}{2018} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{1-\frac{1}{1-\frac{1}{\frac{2018-1}{2018}}}}$$

Subtract 1 from 2018 to get 2017.

$$\frac{1}{1-\frac{1}{1-\frac{1}{\frac{2017}{2018}}}}$$

Divide 1 by \frac{2017}{2018} by multiplying 1 by the reciprocal of \frac{2017}{2018}.

$$\frac{1}{1-\frac{1}{1-1\times \frac{2018}{2017}}}$$

Multiply 1 and \frac{2018}{2017} to get \frac{2018}{2017}.

$$\frac{1}{1-\frac{1}{1-\frac{2018}{2017}}}$$

Convert 1 to fraction \frac{2017}{2017}.

$$\frac{1}{1-\frac{1}{\frac{2017}{2017}-\frac{2018}{2017}}}$$

Since \frac{2017}{2017} and \frac{2018}{2017} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{1-\frac{1}{\frac{2017-2018}{2017}}}$$

Subtract 2018 from 2017 to get -1.

$$\frac{1}{1-\frac{1}{-\frac{1}{2017}}}$$

Divide 1 by -\frac{1}{2017} by multiplying 1 by the reciprocal of -\frac{1}{2017}.

$$\frac{1}{1-1\left(-2017\right)}$$

Multiply 1 and -2017 to get -2017.

$$\frac{1}{1-\left(-2017\right)}$$

The opposite of -2017 is 2017.

$$\frac{1}{1+2017}$$

Add 1 and 2017 to get 2018.

$$\frac{1}{2018}$$

Factor

$$\frac{1}{2 \cdot 1009} = 0.0004955401387512388$$