Answer
$p$ is not a negative integer.
Work Step by Step
Apply the Test of Divergence to find the value of $p$ for the given alternating series.
When $p\geq 0$
Then $\lim\limits_{n \to \infty}\dfrac{1}{n+p}=0$ . This means that the limit $0$ satisfies all the conditions for the alternating series test.
Thus, the series will converge by the Test of Divergence.
When When $p \lt 0$
Then the limit for $\lim\limits_{n \to \infty}\dfrac{1}{n+p}$ will be undefined because $n=-p$ . Thus, the series will not converge by the Test of Divergence.
However, for the negative values, the denominator would not become $0$.
Hence, the value of $p$ can be any real value but $p$ is not a negative integer.
