Let's have the following sequence of fractions: $\frac{24}{17}, \frac{816}{577}, \frac{941664}{665857}, ?$.

What is the next fraction in this sequence?


1 Answer 1


The next one is


This is best explained

here. They appear to be related to Newton's method of calculation of $\sqrt 2$.

  • $\begingroup$ I got the same answer. For those who have a hard time understanding the link posted by @WhatsUp, the next denominator in the pattern seems to be the denominator^2 times 2 minus 1. And for the numerator, you multiply the denominator by ~1.41421356237 to calculate. $\endgroup$
    – Joe Kerr
    Mar 15, 2021 at 0:50
  • $\begingroup$ The formula is $\frac{2ab}{(a^2)/2+b^2}$. $\endgroup$ Mar 15, 2021 at 1:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.