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Theorem. Suppose that an converges to A ER and that be converges to BER. Then, n=1 n=1 1. E 2. can converges to CAV CER. {an+bn} converges to A + BER. Prove the above theorem using results about the limits of sequences (Hint: Consider the partial sums).

Theorem. Suppose that an converges to A ER and that be converges to BER. Then, n=1 n=1 1. E 2. can converges to CAV CER. {an+bn} converges to A + BER. Prove the above theorem using results about the limits of sequences (Hint: Consider the partial sums).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 74E
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Question 7: Recall the following theorem from the lectures: Theorem. Suppose that 1 an converges to A ER and that be converges to BER. Then, n=1 1. E 2. n=1 can converges to CAV CER. {an + bn} converges to A + BER. Prove the above theorem using results about the limits of sequences (Hint: Consider the partial sums).
Transcribed Image Text:Question 7: Recall the following theorem from the lectures: Theorem. Suppose that 1 an converges to A ER and that be converges to BER. Then, n=1 1. E 2. n=1 can converges to CAV CER. {an + bn} converges to A + BER. Prove the above theorem using results about the limits of sequences (Hint: Consider the partial sums).
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