Question

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)

Answer 1

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.