In this section, we introduce a shorthand to abbreviate the “expanded” series form
\[u_m + u_2 + \dots + u_n\]
The way to make this series look compact is by exploiting the sigma notation:
\[u_m + u_2 + \dots + u_r + \dots + u_n := \sum_{r=m}^{n} u_r\]
We now inspect the different parts of the sigma notation:
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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 \(n-m+1\).

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

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

\[u_m + u_2 + \dots + u_r + \dots + u_n := \sum_{r=m}^{n} u_r\]

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 \(n-m+1\).

Sigma notation

Sigma notation