(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the sequence {x_k} = {(arctan(k^2+1),sink)} in R^2. Is there a convergent

subsequence? Justify your answer.

2. Relevant equations

Every bounded sequence in R^n has a convergent subsequence.

3. The attempt at a solution

To show {x_k} is bounded: The range of arctan(k^2+1) is (-pi/2, pi/2) and the range of sin(k) is [-1,1].

A sequence is bded from above and below if there exist an M and an m both belong to R, such that a_k<=M and a_k>=m for all a_k in the sequence. Here, I want to state let M=1 and m=-1. because they are max and min y coordinate value for {x_k}, is this correct?

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# Homework Help: Easy convergent subsequence question.

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