Answer
(a) A geometric series is a series in the form of $\Sigma_{n=0}^{\infty}ar^{n}$ with initial term $a$ and common ratio $r$.
It converges if $|r| \lt 1$ . In that case, it converges to $\frac{a}{1-r}$
(b) A $p$-series is a series in the form of $\Sigma_{n=1}^{\infty}\frac{1}{n^{p}}$, where p is a constant . It converges if $p \gt1$
Work Step by Step
(a) A geometric series is a series in the form of $\Sigma_{n=0}^{\infty}ar^{n}$ with initial term $a$ and common ratio $r$.
It converges if $|r| \lt 1$ . In that case, it converges to $\frac{a}{1-r}$
(b) A $p$-series is a series in the form of $\Sigma_{n=1}^{\infty}\frac{1}{n^{p}}$, where p is a constant . It converges if $p \gt1$
