Geometric Series: A series of the form $\sum_{n=0}^{\infty} ar^n$, where each term is obtained by multiplying the previous term by a fixed non-zero number $r$.
Harmonic Series: $\sum_{n=1}^{\infty} \frac{1}{n}$, which is known to diverge because its partial sums grow without bound.
Ratio Test: A test for determining the convergence or divergence of a series by examining the limit $\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|$.