Sigma notation

In this section, we introduce a shorthand to abbreviate the “expanded” series form

\[u_m + u_{m+1} + \dots + u_n\]

The way to make this series look compact is by exploiting the sigma notation:

\[u_m + u_{m+1} + \dots + u_r + \dots + u_n := \sum_{r=m}^{n} u_r\]

We now inspect the different parts of the sigma notation:

Note: The running index r will take all (consecutive) integer values from the lower limit \(m\) to the upper
limit \(n\) . The number of terms in a series is equal to \(n-m+1\).