Construct two divergent sequences (xn)n≥1 and (yn)n≥1 such that (xn + yn)n≥1 converges
Question
Solution 1
Sure, here is an example of two divergent sequences whose sum converges:
Let's define the sequences (xn)n≥1 and (yn)n≥1 as follows:
xn = n for all n≥1 yn = -n for all n≥1
Clearly, both sequences are divergent as n tends to infinity. However, their sum (xn + yn)n≥1 is equal to 0 for all n≥1, which Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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