We prove if a sequence a_n converges to 0, and a sequence b_n is bounded, then the sequence of products of their terms, a_n * b_n, converges to 0. This is what we could call an extra sequence limit law! We'll see examples showing a_n converging to 0 alone does not force a_n * b_n to converge, and also see how b_n doesn't necessarily HAVE to be bounded, but if it is then we know a_n * b_n converges to 0, which is what we prove using a pretty typical convergent sequence proof. #RealAnalysis
Absolute Value Definition of a Bounded Sequence: • Absolute Value Definit...
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Негізгі бет Bounded Sequence and Zero Convergent Sequence Limit Law | Real Analysis Exercises
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