In this video I now introduce you to the standard result for the sum of cubed terms, ∑r3.
It can be shown (see proof by induction) that

Formulae to remember:

  • \sum\limits_{r = 1}^n {{r^3}}  = \frac{{{n^2}}}{4}{\left( {n + 1} \right)^2}

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.

Examples in the video

Evaluate the following:

  1. \sum\limits_{r = 1}^8 {{r^3}}
  2. \sum\limits_{r = 1}^{2N} {5{r^3}}
  3. 3{\left( 5 \right)^3} + 3{\left( 6 \right)^3} + 3{\left( 7 \right)^3} + ... + 3{\left( {10} \right)^3}