What sigma notation says _r=mnu_r=u_m+u_m+1+. s+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 - _r=25(3r-1)=5+8+11+14=38 - _k=042k=1+2+4+8+16=31 - _j=-21j2=4+1+0+1=6 Fast checks before moving on - Did you include both endpoints? - 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?

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

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.

\(\sum\limits_{r=2}^{5}(3r-1)=5+8+11+14=38\)

\(\sum\limits_{k=0}^{4}2^k=1+2+4+8+16=31\)

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?

Sequence and Series

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Sigma notation: read, count and expand

Sigma notation: read, count and expand