How can I find the value of n such that (4n-2)/(7n-3) is within 10^-2 of its limit 4/7 . I know you set (4n-2)/(7n-3)-4/7 < 10^-2 but I can seem to rearrange it, thanks
Hi jpquinn91,
You will need to write the difference the other way around.
$\displaystyle \frac{4}{7}-\frac{4n-2}{7n-3}<10^{-2}$
$\displaystyle 4(7n-3)-7(4n-2)<7(7n-3)10^{-2}$ if 7n>3
$\displaystyle 28n-12-28n+14<(49n-21)10^{-2}$
$\displaystyle 200<49n-21$
$\displaystyle 49n>221$
$\displaystyle n>\frac{221}{49}$
n=5 or so.
$\displaystyle \frac{4}{7}-\frac{18}{32}=0.00892$