#### Answer

$p$ is not a negative integer.

#### Work Step by Step

1. We will have to apply the Test of Divergence to find the value of $p$ for the given alternating series when $p\geq 0$
So, $\lim\limits_{n \to \infty}\dfrac{1}{n+p}=0$
This implies that the limit $0$ satisfies all the condition for alternating series test and converge by the Test of Divergence.
2. We will have to apply the Test of Divergence to find the value of $p$ for the given alternating series when $p\geq 0$
$p \lt 0$
Here, $\lim\limits_{n \to \infty}\dfrac{1}{n+p}$ the limit is undefined because $n=-p$ , that is, the series will not converge by the Test of Divergence.
But the denominator will not become $0$ for the negative values. This implies that $p$ can be any real value but the value of $p$ can not be a negative integer.