An infinite sequence is a never-ending list of elements, where each element is associated with a positive integer index and there is no last element in the sequence.

Mathematically, an infinite sequence can be represented as:

\$ a = (a_1, a_2, a_3, ...) . \$

Explanation: Here, 'a' is the name of the sequence, and \$ a_1, a_2, a_3, ... \$ are the individual elements of the sequence.

An infinite series is a mathematical representation of the sum of an infinite sequence of numbers. It is denoted by the following general form:

\$ S = a_1 + a_2 + a_3 + a_4 + ... \$ .

Explanation: Here, 'S' represents the sum of the infinite series, and '\$ a_1, a_2, a_3, ... \$' are the individual terms of the sequence.