Question Number 12106 by tawa last updated on 13/Apr/17
Answered by FilupS last updated on 13/Apr/17
$$\Sigma{a}_{{n}} \:\mathrm{diverges}\:\mathrm{if}:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} \neq\mathrm{0} \\ $$$$\Sigma{ca}_{{n}} ={c}\Sigma{a}_{{n}} \\ $$$$\therefore{c}\Sigma{a}_{{n}} \:\mathrm{diverges} \\ $$$$\because\Sigma{a}_{{n}} \rightarrow\pm\infty \\ $$
Commented by tawa last updated on 13/Apr/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$