We prove the limit law for a constant multiplied by a convergent sequence. If a_n converges to a and c is a real number, then the sequence c*a_n converges to c*a. As in, the constant multiple of a convergent sequence converges to its limit multiplied by the same constant. This is a straightforward proof using the epsilon definition of a convergent sequence, except for the case where c is 0. If c = 0, our result follows from the fact that a convergent sequence converges to its constant value.
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Негізгі бет Proof: Limit Law for Constant Times a Convergent Sequence | Real Analysis
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