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.

Examples:


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

Properties:


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

Example:

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