Question Number 159962 by bounhome last updated on 23/Nov/21
$${show}\:{me}:\:{these}\:{are}\:{the}\:{cauchy}\:{criterion}.\:{please} \\ $$$$\mathrm{1}.\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$$$\mathrm{2}.\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{1}}{\mathrm{3}!}+...+\frac{\mathrm{1}}{{n}!}\right) \\ $$$$\mathrm{3}.\:\left(\left(−\mathrm{1}\right)^{{n}} \right) \\ $$$$\mathrm{4}.\:{n}+\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}} \\ $$$$\mathrm{5}.\left(\mathrm{1}{nm}\right) \\ $$$$ \\ $$