Question

Find a series of fractions converging to $.24226$, the excess in days of the true tropical year over $365days$.

Answer 1

To find a series of fractions converging to $0.24226$

Here , The Continued fraction corresponding to $0.24226$ is

$\frac{1}{4+}\frac{1}{7+}\frac{1}{1+}\frac{1}{4+}\frac{1}{1+}.....$

Also , the first five Convergents are

$\frac{1}{4},\frac{7}{29},\frac{8}{33},\frac{39}{161},\frac{47}{194}$