Construct two divergent sequences (xn)n≥1 and (yn)n≥1 such that (xn + yn)n≥1 converges

Question

Construct two divergent sequences (xn)n≥1 and (yn)n≥1 such that (xn + yn)n≥1 converges
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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

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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