If a sequence is both bounded and monotonic, then the sequence converges.

$${a_n}^\infty_1$$

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

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

A sequence converges if its limit as n approaches infinity exists and is a finite number. It approaches a specific value.

A sequence diverges if its limit as n approaches infinity does not exist (oscillates) or is infinite. It does not approach a specific value.

A sequence is a list of numbers, while a series is the sum of the numbers in a sequence.

The sum of the infinite terms approaches a finite value.

The sum of the infinite terms does not approach a finite value; it either goes to infinity or oscillates.