Solve 1/1+frac{1{2020}}+1/1+1{1+frac{1/2020}}

$$\frac{ 1 }{ 1+ \frac{ 1 }{ 2020 } } + \frac{ 1 }{ 1+ \frac{ 1 }{ 1+ \frac{ 1 }{ 2020 } } }$$

Evaluate

$$\frac{12247261}{8166861}\approx 1.499628927$$

Solution Steps

Convert 1 to fraction \frac{2020}{2020}.

$$\frac{1}{\frac{2020}{2020}+\frac{1}{2020}}+\frac{1}{1+\frac{1}{1+\frac{1}{2020}}}$$

Since \frac{2020}{2020} and \frac{1}{2020} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{2020+1}{2020}}+\frac{1}{1+\frac{1}{1+\frac{1}{2020}}}$$

Add 2020 and 1 to get 2021.

$$\frac{1}{\frac{2021}{2020}}+\frac{1}{1+\frac{1}{1+\frac{1}{2020}}}$$

Divide 1 by \frac{2021}{2020} by multiplying 1 by the reciprocal of \frac{2021}{2020}.

$$1\times \frac{2020}{2021}+\frac{1}{1+\frac{1}{1+\frac{1}{2020}}}$$

Multiply 1 and \frac{2020}{2021} to get \frac{2020}{2021}.

$$\frac{2020}{2021}+\frac{1}{1+\frac{1}{1+\frac{1}{2020}}}$$

Convert 1 to fraction \frac{2020}{2020}.

$$\frac{2020}{2021}+\frac{1}{1+\frac{1}{\frac{2020}{2020}+\frac{1}{2020}}}$$

Since \frac{2020}{2020} and \frac{1}{2020} have the same denominator, add them by adding their numerators.

$$\frac{2020}{2021}+\frac{1}{1+\frac{1}{\frac{2020+1}{2020}}}$$

Add 2020 and 1 to get 2021.

$$\frac{2020}{2021}+\frac{1}{1+\frac{1}{\frac{2021}{2020}}}$$

Divide 1 by \frac{2021}{2020} by multiplying 1 by the reciprocal of \frac{2021}{2020}.

$$\frac{2020}{2021}+\frac{1}{1+1\times \frac{2020}{2021}}$$

Multiply 1 and \frac{2020}{2021} to get \frac{2020}{2021}.

$$\frac{2020}{2021}+\frac{1}{1+\frac{2020}{2021}}$$

Convert 1 to fraction \frac{2021}{2021}.

$$\frac{2020}{2021}+\frac{1}{\frac{2021}{2021}+\frac{2020}{2021}}$$

Since \frac{2021}{2021} and \frac{2020}{2021} have the same denominator, add them by adding their numerators.

$$\frac{2020}{2021}+\frac{1}{\frac{2021+2020}{2021}}$$

Add 2021 and 2020 to get 4041.

$$\frac{2020}{2021}+\frac{1}{\frac{4041}{2021}}$$

Divide 1 by \frac{4041}{2021} by multiplying 1 by the reciprocal of \frac{4041}{2021}.

$$\frac{2020}{2021}+1\times \frac{2021}{4041}$$

Multiply 1 and \frac{2021}{4041} to get \frac{2021}{4041}.

$$\frac{2020}{2021}+\frac{2021}{4041}$$

Least common multiple of 2021 and 4041 is 8166861. Convert \frac{2020}{2021} and \frac{2021}{4041} to fractions with denominator 8166861.

$$\frac{8162820}{8166861}+\frac{4084441}{8166861}$$

Since \frac{8162820}{8166861} and \frac{4084441}{8166861} have the same denominator, add them by adding their numerators.

$$\frac{8162820+4084441}{8166861}$$

Add 8162820 and 4084441 to get 12247261.

$$\frac{12247261}{8166861}$$

Factor

$$\frac{13 ^ {2} \cdot 72469}{3 ^ {2} \cdot 43 \cdot 47 \cdot 449} = 1\frac{4080400}{8166861} = 1.499628927197365$$