Answer
Converges
Work Step by Step
Root Test states that when $\Sigma a_k$ is an infinite series with positive terms and, then $r=\lim\limits_{k \to \infty}\sqrt[k] a_k$
a) When $0 \leq r \lt 1$, the series converges. (b) When $r \gt 1$, or, $\infty$, so the series diverges. (c) When $r=1$, the ratio test is inconclusive.
Now, $r=\lim\limits_{k \to \infty}(\dfrac{1}{1+p})^1$
We can see that for $p \gt0 \implies \dfrac{1}{1+p} \lt 1$
Therefore, the series converges by the root test.
