Rational sequence/2x-1 divided by 3x-4/Effort number/Exercise

Determine for the sequence

${}x_{n}:={\frac {2n+1}{3n-4}}\,$

and for

${}\epsilon ={\frac {1}{10}},\,{\frac {1}{100}},\,{\frac {1}{1000}}\,,$

for which (minimal) ${}n$ the estimate

${}\vert {x_{n}-{\frac {2}{3}}}\vert \leq \epsilon \,$

holds.

Create a solution