Question

Express the following quantities as continued fractions and find the fourth convergent to each.
$\frac{832}{159}$

Answer 1

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

$\frac{832}{159}$

This can be written as

$5+\frac{37}{159}$

$\therefore$ the Successive quotients are $4,3,2,1$

and This can be written as Continued fraction

$\frac{832}{159}=5+\frac{1}{4+}\frac{1}{3+}\frac{1}{2+}\frac{1}{1+}\frac{1}{3};$

Here , the fourth convergent is $\frac{157}{30}$