In this video I now introduce you to the standard result for the sum of squared terms, ∑r2. It can be shown (see proof by induction) that

Formulae to remember:

  • \sum\limits_{r = 1}^n {{r^2}}  = \frac{n}{6}\left( {2n + 1} \right)\left( {n + 1} \right)

and based on this result I 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.

Evaluate the following:

  1. \sum\limits_{r = 1}^{10} {{r^2}}
  2. \sum\limits_{r = 1}^n {\left( {6{r^2} + 5} \right)}
  3. 2{\left( 8 \right)^2} + 2{\left( 9 \right)^2} + 2{\left( {10} \right)^2} + ... + 2{\left( {15} \right)^2}