Answer
a) $-1, 1, -1, 1$
b) Limit does not exist
Work Step by Step
$$\sum_{k=1}^{\infty} cos(\pi k)$$
Part A)
$a_1 = cos(\pi (1)) = -1$
$a_2 = cos(\pi (2)) = 1$
$a_3 = cos(\pi (3)) = -1$
$a_4 = cos(\pi (4)) = 1$
First four terms: $-1, 1, -1, 1$
Part B)
The sequence does not seem to converge, since the term values are simply alternating between $1$ and $-1$.
