Question

What is the summation notation?

Answer 1

A simple method for indicating the sum of a finite (ending) number of terms in a sequence is the summation notation. This involves the Greek letter sigma, \(\Sigma\). When using the sigma notation, the variable defined below the \(\sum\) is called the index of summation. The lower number is the lower limit of the index (the term where the summation starts), and the upper number is the upper limit of the summation (the term where the summation ends). Consider
\[
\sum_{k=2}^{7}(2 k+3)
\]
This is read as "the summation of \((2 k+3)\) as \(k\) goes from 2 to 7 ". The replacements for the index are always consecutive integers.
\[
\begin{aligned}
\sum_{k=2}^{7}(2 k+3) &=[2(2)+3]+[2(3)+3]+\left[2(4)^{k=3}+3\right]+[2(5)+3]+[2(6)+3]+[2(7)+3] \\
&=7+9+11+13+15+17 \\
&=72
\end{aligned}
\]