Answer
a) First Four Terms: $-1, 1, -2,2$
b) Limit doesn't exist
Work Step by Step
$$\sum_{k=1}^{\infty} k(-1)^k$$
Part A)
$a_1 = 1(-1)^1 = -1$
$a_2 = -1 + 2(-1)^2 = 1$
$a_3 = 1 + 3(-1)^3 = -2$
$a_4 = -2 + 4(-1)^4 = 2$
Part B)
Limit doesn't exist because it's a divergent sequence.
