Question

Express the following surds as continued fractions, and find the sixth convergent to $\sqrt{5}$.

Answer 1

$x^2-{5y}^2=1$

The sixth convergent for $\sqrt{5}$ are

$\frac{2}{1},\frac{7}{3},\frac{9}{4},\frac{10}{9},\frac{29}{13},\frac{38}{17}$

So, the sixth convergent is $is\frac{38}{17}$