- #1
pantin
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Homework Statement
Consider the sequence {x_k} = {(arctan(k^2+1),sink)} in R^2. Is there a convergent
subsequence? Justify your answer.
Homework Equations
Every bounded sequence in R^n has a convergent subsequence.
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?