Introduction. Before we can calculate symbolically a Riemann sum, we need to recall some properties of sums and summation symbols.

Definition. Let f be a function whose domain includes the integers from n through m. We define

We call i the index of summation, n is the lower limit of summation, and m is the upper limit of summation.


  1. Discussion [Using Flash] [Using Java]

  2. Discussion [Using Flash] [Using Java]

You can use the TI-85 or TI-86 graphing calculator or a MathView Notebook to evaluate summations.


  1. Discussion

  2. Discussion [Using Flash] [Using Java]

  3. Discussion [Using Flash] [Using Java]

  4. Discussion

  5. Discussion
You can determine more formulas like the properties above by using a computer algebra system as Maple.


  1. Evaluate
    Discussion [Using Flash] [Using Java]