By considering the sequence of partial sums calculate the limit of $\sum^{\infty}_{n=0} p^n$ , where $0

Question

I have no idea how to solve this problem. I know that the definition states that a series $$\sum^\infty_{k=1}=a_1+a_2+a_3+a_4+........$$ is convergent if the sequence of partial sums $$S_n=a_1+a_2+a_3+......+a_n = \sum_{k=1}^n a_k$$ converges to a limit, so $$\lim_{n\to\infty}S_n$$ And the limit is called the sum of the series denoted by $$\sum_{k=1}^{\infty}a_k=S$$ However, i do not then know how to implement this into other promblems like the one below, $$\sum^{\infty}_{n=0}p^n$$ Thank you.