Theorem: Algebra on Series

Let and be two absolutely convergent series. Then:
  1. The sum of the two series is again absolutely convergent. Its limit is the sum of the limit of the two series.
  2. The difference of the two series is again absolutely convergent. Its limit is the difference of the limit of the two series.
  3. The product of the two series is again absolutely convergent. Its limit is the product of the limit of the two series (Cauchy Product ).

Proof:

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