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, ...
$\displaystyle t_n = \frac {n+3}{2n+4}$, 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.