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Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer...

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) a n = n 3 /n + 2

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Answer #1

The given sequence is

In order to determine whether the sequence converges or diverges, we need to examine the behaviour of the sequence as n approaches infinity.

We have,

As n approaches infinity, the numerator tends to 1 and the denominator tends to 0. Thus,

Hence, the given sequence diverges and its limit does not exist.

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