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Rational sequence/2x-1 divided by 3x-4/Effort number/Exercise
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Determine for the sequence
x
n
:=
2
n
+
1
3
n
−
4
{\displaystyle {}x_{n}:={\frac {2n+1}{3n-4}}\,}
and for
ϵ
=
1
10
,
1
100
,
1
1000
,
{\displaystyle {}\epsilon ={\frac {1}{10}},\,{\frac {1}{100}},\,{\frac {1}{1000}}\,,}
for which (minimal)
n
{\displaystyle {}n}
the estimate
|
x
n
−
2
3
|
≤
ϵ
{\displaystyle {}\vert {x_{n}-{\frac {2}{3}}}\vert \leq \epsilon \,}
holds.
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