Can anyone come up with a formula for this sequence:

3/4, 2/3, 5/8, 3/5, 7/12, 4/7, 9/16, 5/9, 11/20, 6/11, ...

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- Mar 10th 2008, 09:16 PMjzelltsequence pattern
Can anyone come up with a formula for this sequence:

3/4, 2/3, 5/8, 3/5, 7/12, 4/7, 9/16, 5/9, 11/20, 6/11, ... - Mar 10th 2008, 09:49 PMbadgerigar
$\displaystyle t_n = \frac {n+3}{2n+4}$, assuming that the first term listed is $\displaystyle t_0$.

This becomes obvious if you multiply the odd terms by $\displaystyle \frac {2}{2}$. I found this after looking at only the odd and even terms and spotting a pattern there.