A series means adding up numbers within a sequence.

Sigma notation is shorthand for summing up a series.

For example:

\(\displaystyle\sum_{r=1}^n 1 = \overbrace{1+1+...+1+1}^{\text{n times}} = n\)

\(\displaystyle\sum_{r=1}^n r = \dfrac{n(n+1)}{2}\)

\(\displaystyle\sum_{r=1}^5 r^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55 \)

General result

\(\displaystyle\sum_{r=1}^n f(x) = f(1) + f(2) + ... + f(n-1) + f(n) \)