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?
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asked Mar 15, 2021 at 0:23
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1 Answer
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The next one is
$\frac{1254027132096}{886731088897}$.
This is best explained
here. They appear to be related to Newton's method of calculation of $\sqrt 2$.
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$\begingroup$ 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 KerrCommented Mar 15, 2021 at 0:50
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$\begingroup$ The formula is $\frac{2ab}{(a^2)/2+b^2}$. $\endgroup$ Commented Mar 15, 2021 at 1:01