Question Number 76577 by Rio Michael last updated on 28/Dec/19
$$\:{given}\:{a}\:{sequence}\:{defined}\:{by}\:\:\left\{\frac{\mathrm{3}{n}}{\mathrm{2}{n}+\:\mathrm{5}}\right\}_{{n}=\mathrm{1}} ^{\infty} ,\:{does}\:{this}\: \\ $$$${sequence}\:{converge}\:{or}\:{diverge},\:{explain} \\ $$
Answered by john santu last updated on 28/Dec/19
$${converge}.\:\:\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\left\{\frac{\mathrm{3}{n}}{\mathrm{2}{n}+\mathrm{5}}\right\}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${so}\:\left\{\frac{\mathrm{3}{n}}{\mathrm{2}{n}+\mathrm{5}}\right\}\underset{{n}=\mathrm{1}} {\overset{\propto} {\:}}\:{converge}\:{to}\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$