Proof: Limit Law for Product of Convergent Sequences | Real Analysis
We prove the limit law for the product of convergent sequences. If a_n converges to a and b_n converges to b, then the sequence a_n*b_n converges to a*b. As in, the product of convergent sequences converges to the product of their limits. This is a slightly tricky proof using the epsilon definition of a convergent sequence, and absolute value manipulations!
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