Understanding Diverging Sequences and Limits

Diverging means that the two sequences are moving away from each other. In other words, the terms of the two sequences are increasing at different rates.

For example, if we have two sequences $a_n$ and $b_n$, and $a_n = 2^n$ and $b_n = n^2$, then the sequences are diverging because the terms of one sequence (in this case, $a_n$) are increasing much faster than the terms of the other sequence (in this case, $b_n$).

In the context of limits, if a sequence converges to a limit, then the sequence is said to converge to that limit "as" or "to" the limit. If the sequence does not converge to any limit, then it is said to diverge.

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