True-False Quiz Question 15: Divergent Sequences Can Multiply to Fo...

In this video I show that we can multiply 2 divergent sequences to form a convergent sequence. The example I use is the sequence with terms (-1)ⁿ, which is a divergent sequence that alternates between 1 and - 1 as n approaches infinity. If we multiply this sequence by itself, hence multiplying 2 divergent sequences, we end up with 1^n which equals 1 for all values of n. Thus the new sequence is convergent, and the answer to the question is False: multiplying divergent sequences does not necessarily mean we get a divergent sequence.

Time stamps:

Question 15: 0:00
Solution: False: 0:10
Divergent sequences (-1)ⁿ multiply to form a convergent sequence: 0:17

Full video below:

Infinite Sequences and Series: Review and True-False Quiz:
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True-False Quiz Question 15: Divergent Sequences Can Multiply to Form a Convergent Sequence