Unit 5.3: Sigma Notation

  • The mathematical symbol is the capital letter S in Greek alphabet. It is used as the symbol for the sum of a series.

  • Note that the last value you substitute is not always giving the number of terms that will be added.
  • The number of terms = Top – Bottom + 1
  • What is the number of terms in this series?
  • The answer will therefore be: 20 – 3 + 1 = 18, so we will calculate the sum of 18 terms in the series.

Infinite geometric series

  • A Geometric series can also have smaller and smaller values.
  • What happens when .
  • Therefore the series will converge to a number referred to as the sum to infinity. This is the case only if -1 < r < 1
  • Example: 9; 3; 1…
  • therefore: the series converges and the sum to infinity exists

Formula for sum to infinity