$${a_n}^\infty_1$$

$$s_n = \sum_{i=1}^{n} a_i$$

$$s_\infty = \lim\limits_{n \to \infty} \sum_{i=1}^{n} a_i$$

1. Find the limit as n approaches infinity. 2. If the limit exists and is finite, it converges. 3. If the limit does not exist or is infinite, it diverges.

1. Calculate $a_1, a_2, a_3$. 2. $s_1 = a_1$. 3. $s_2 = a_1 + a_2$. 4. $s_3 = a_1 + a_2 + a_3$.

A list of terms related by a common pattern.

A sequence where $\lim_{n \to \infty} a_n$ exists and is finite.

A sequence where $\lim_{n \to \infty} a_n$ does not exist or is infinite.

A sequence where $\frac{a_{n+1}}{a_n} > 1$ for all n.

A sequence where $\frac{a_{n+1}}{a_n} < 1$ for all n.

A sequence that is either increasing or decreasing.

There exists an upper bound to the sequence.

There exists a lower bound to the sequence.

A sequence that is both bounded above and below.

A sum of the terms in a sequence.

The value of the summation of the 1st through the $n^{th}$ terms.

A series where n=$infty$, or $s_\infty = \lim\limits_{n \to \infty} \sum_{i=1}^{n} a_i$.

A series in which $s_\infty$ exists and is finite.

A series in which $s_\infty$ does not exist or is infinite.

A series where the middle terms cancel out, leaving only the first and last terms.