To add the terms of a sequence, we replace each comma between the terms with a plus sign, forming what is called a series. Because each sequence is infinite, the number of terms in the series associated with it is infinite also. Two examples of infinite series are:

1^{2}+2^{2}+3^{2}+4^{2}+...+n^{2}+...

1+3+5+7+...+(2n+1)+...

There is a shorthand method of indicating the sum of the first n terms, or the nth partial sum of a sequence. This method, called summation notation, involves the symbol which is capital sigma in the Greek alphabet.

The expression designates the sum of the five terms obtained if we successively substitute the natural numbers 1, 2, 3, 4 and 5 for n in the expression n^{2}. Hence,