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.
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