What sigma notation says
\[\sum_{r=m}^{n}u_r=u_m+u_{m+1}+\cdots+u_n\]
The index \(r\) takes every integer value from \(m\) to \(n\). The number of terms is \(n-m+1\). The letter used for the index is a dummy variable.
Three quick examples
<ol><li>\(\sum_{r=2}^{5}(3r-1)=5+8+11+14=38\)</li><li>\(\sum_{k=0}^{4}2^k=1+2+4+8+16=31\)</li><li>\(\sum_{j=-2}^{1}j^2=4+1+0+1=6\)</li></ol>
Fast checks before moving on
<ul><li>Did you include both endpoints?</li><li>If the lower limit is \(0\), did you include the zero-index term?</li><li>When changing an index, did you transform the term and both limits together?</li></ul>

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

The index \(r\) takes every integer value from \(m\) to \(n\). The number of terms is \(n-m+1\). The letter used for the index is a dummy variable.

If the lower limit is \(0\), did you include the zero-index term?

When changing an index, did you transform the term and both limits together?

Mathematics

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Sigma notation: read, count and expand

Sigma notation: read, count and expand