True-False Quiz Question 15: Divergent Sequences Can Multiply to Form a Convergent Sequence
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:
- HIVE video notes: @mes/infinite-sequences-and-series-review-and-true-false-quiz
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