Question Number 84215 by mathocean1 last updated on 10/Mar/20
$${hi} \\ $$$${show}\:{that}\:{the}\:{following}\:{sequence} \\ $$$${is}\:{limited}: \\ $$$${U}_{{n}} =\frac{\mathrm{3}{n}+\mathrm{2}}{\mathrm{2}{n}+\mathrm{1}} \\ $$$${precise}\:{the}\:{upper}\:{and}\:{lower}. \\ $$
Answered by Rio Michael last updated on 10/Mar/20
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:{U}_{{n}} \:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{3}{n}\:+\:\mathrm{2}}{\mathrm{2}{n}\:+\:\mathrm{1}}\:=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$