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AfilCa [17]
2 years ago
5

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)

an = 4n cos(7nπ)
Mathematics
1 answer:
In-s [12.5K]2 years ago
5 0

Answer:

The sequence diverges.

Step-by-step explanation:

A sequence a_{n} converges when \lim_{n \rightarrow \infty} a_{n} is a real number.

In this question, the sequence given is:

a_{n} = 4n\cos{(7n\pi)}

The cosine is always going to be between -1 and 1, so for the convergence of the sequence, we look it as: a_{n} = 4n. So

\lim_{n \rightarrow \infty} a_{n} = \lim_{n \rightarrow \infty} 4n = \infty

Since the limit is not a real number, the sequence diverges.

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