Question

Express the following quantities as continued fractions and find the fourth convergent to each.
$\frac{253}{179}$

Answer 1

To Express the following quantities as continued fractions and to find the fourth convergent to each .

$\frac{253}{179}$

This can be written as

$1+\frac{74}{179}$

$\therefore$ the Successive quotients are $2,2,2,1,1,2$

and This can be written as Continued fraction

$\frac{253}{179}=1+\frac{1}{2+}\frac{1}{2+}\frac{1}{2+}\frac{1}{1+}\frac{1}{1+}\frac{1}{2+}\frac{1}{2};$

Here , the fourth convergent is $\frac{17}{12}$

Hence , fourth Convergent is $\frac{17}{12}$