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JH
Numerade Educator

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Problem 61 Easy Difficulty

Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the margin note on page 699 for advice on graphing sequence .)
$ a_n = \frac {n^2 \cos n}{1 + n^2} $

Answer

divergent,

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Video Transcript

Let's use a graph of the sequence and to predict weather, a convergence or diverges. Now look here and gizmos. We have a graph. You could see our formula for am. Now we've graft the first seventy six terms, and based on the looks, it looks like this thing does not converge. But it's more or less bouncing around between negative one one. So Betweennegative one and and one sense the limit. It's and goes to infinity of n squared over one plus and squared equals one, sir, So A N is approximately equal to co sign in for a large and and the limit of co sign n does not exist. Therefore, a N is divergent again. It's diversion because its limit doesn't exist, and that's our final answer.