Maths At Warwick
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Maths At Warwick

On Subsequences

MA141 Analysis 1

Studying Mathematics at Warwick University

I just completed the second assignment in Analysis. I came across a question on the convergence of sequences and subsequences.

Give this problem a try before jumping in for the solution!

Solution

We are given that a subsequence of the sequence an converges to l. That means there exists an R in the natural numbers such that for all r > R, we have

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