Let (an) be the sequence given byan = 1√2n + 1 − 1√2nProve from first principles that (an) is Cauchy.

Question

Let (an) be the sequence given byan = 1√2n + 1 − 1√2nProve from first principles that (an) is Cauchy.
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Solution 1

To prove that a sequence (an) is Cauchy, we need to show that for any given positive number ε, there exists a positive integer N such that for all integers m, n greater than N, the absolute difference between am and an is less than ε.

Given the sequence an = 1/√(2n + 1) - 1/√(2n), let's simplify it 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.
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