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Question Number 12106 by tawa last updated on 13/Apr/17

Answered by FilupS last updated on 13/Apr/17

Σa_n  diverges if:    lim_(n→∞)  a_n ≠0  Σca_n =cΣa_n   ∴cΣa_n  diverges  ∵Σa_n →±∞

$$\Sigma{a}_{{n}} \:\mathrm{diverges}\:\mathrm{if}:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} \neq\mathrm{0} \\ $$$$\Sigma{ca}_{{n}} ={c}\Sigma{a}_{{n}} \\ $$$$\therefore{c}\Sigma{a}_{{n}} \:\mathrm{diverges} \\ $$$$\because\Sigma{a}_{{n}} \rightarrow\pm\infty \\ $$

Commented by tawa last updated on 13/Apr/17

God bless you sir.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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