Answer
a) First Four Terms: $-1, 0, -1 ,0$
b) Limit doesn't exist
Work Step by Step
$$\sum_{k=1}^{\infty} (-1)^k$$
Part A)
$a_1 = (-1)^1 = -1$
$a_2 = (-1)^2 = -1 + 1 = 0$
$a_3 = (-1)^3 = 0 + (-1) = -1$
$a_4 = (-1)^4 = -1 + 1 = 0$
Part B)
Limit doesn't exist because the partial sums are simply alternating between the values $-1$ and $0$, and does not approach a single value.
