In this series of videos I continue to extend the work I did earlier on using sigma notation to represent the summation of a series. This video is partly a reminder of that work and then introduces you to the following results based on summing linear terms.

Formulae to remember:

  • \sum\limits_{r = 1}^n {r = \frac{n}{2}\left( {n + 1} \right)}
  • \sum\limits_{r = 1}^n {\left( {ar + b} \right) = a\sum\limits_{r = 1}^n {r + nb} }

Examples

In this video I continue to extend the work I did earlier on using the standard results that I showed in the previous video, and based on these results show you how to tackle the following problems which I would strongly encourage you to try.
Each one I have chosen to reflect something different.

Examples in the video

Evaluate the following:

  1. \sum\limits_{r = 20}^{45} {3r}
  2. \sum\limits_{r = 1}^{2n} {\left( {5r - 4} \right)}
  3. \sum\limits_{r = 10}^{{n^2}} {\left( {2r - 3} \right)}