The infinity symbol in math represents the concept of infinity. For example, the symbol is used in the notation of a limit to denote that the variable grows arbitrarily large, rather than actually assume an infinite value.
The syntax for a limit is a the abbreviation "lim" followed an expression. Underneath the letters "lim" is the value the variable approaches within the expression denoted as the variable with an arrow to the value it is approaching.
A series is the operation of adding an infinite number expressions together. A series is denoted using the summation operator and the index variable k.