Question Number 66932 by Tinkutara@ last updated on 20/Aug/19
$${which}\:{of}\:{the}\:{sequences}\:{converges}\:? \\ $$$$\left.\mathrm{1}\right)\:{a}_{{n}} =\:{n}−\frac{\mathrm{1}}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{a}_{{n}} =\:\left(\left(−\mathrm{1}\right)^{{n}} +\mathrm{1}\right)\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$
Answered by turbo msup by abdo last updated on 21/Aug/19
$$\left.\mathrm{1}\right)\:\left({a}_{{n}} \right){fiverges} \\ $$$$\left.\mathrm{2}\right){a}_{\mathrm{2}{n}} =\mathrm{2}\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}\:\rightarrow\mathrm{2}\:{and}\:{a}_{\mathrm{2}{n}+\mathrm{1}} =\mathrm{0} \\ $$$${so}\:\left({a}_{{n}} \right){diverges} \\ $$