I'm trying to understand divergence of a sequence (not series). What methods can I use to prove divergence? I know that convergence can be proven using various methods, such as squeeze theorem and sum, difference, product and quotient rule etc.(adsbygoogle = window.adsbygoogle || []).push({});

Could I use the following to prove divergence?

If [itex] a_{n} [/itex] is a sequence of real numbers, [itex] f(n) = a_{n} [/itex] and [itex] \lim_{n→∞} f(n) [/itex] does not exist, but is not equal to ∞ or -∞, does [itex] a_{n} [/itex] necessarily diverge?

If [itex] a_{n} [/itex] is a sequence of real numbers, [itex] f(n) = a_{n} [/itex] and [itex] \lim_{n→∞} f(n) = ∞ [/itex], does [itex] a_{n} [/itex] necessarily diverge?

These two ideas will greatly facilitate my understanding of sequence divergence.

Thanks!

BiP

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# Divergence of a sequence

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