Question

Why is the series sigma n=1 to infinity of cos(n) divergent

Answer 1

Because the terms do not approach zero.

Answer 2

what happens as n increases?
do the terms of the series\[\{\cos(n)\}_{n=1
}^\infty\]approach zero?
no, they oscillate forever between 1 and -1, which means we are always adding more and more non-zero terms that do not vanish as \(n\to\infty\), hence the series diverges

Answer 3

\(\cos \theta\) with n being integers:

Answer 4

\[\sum_{n=1}^{\infty} \cos \theta\]