# True-False Quiz Question 15: Divergent Sequences Can Multiply to Form a Convergent Sequence

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• Published on Jan 30, 2024

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

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