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Working With Summation Notation

Working With Summation Notation

Author: c o

To introduce summation notation and to demonstrate its use by examining a number of examples.

The notation is introduced, its parts are labeled, and a few examples of its use are given. The lesson ends with a short section on some algebraic "tricks" that are likely to crop up when working with sums.

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The Notation

Summation notation, or "Sigma notation", is usually used to express sums whose summands are the terms in a sequence.  The notation includes a lower bound and an upper bound that together identify the terms over which the sum occurs.  The notation is used to represent both finite sums and infinite sums.

In the subscript beneath the Sigma can be found the index of the sum and the sum's lower limit.  The lower limit identifies the starting term in our sequence of summands, and the upper limit identifies the final term.

The lower limit is often set to one, but it may be any number that is less than the upper limit.  Moreover, the upper limit is often a number, but it may also be set to infinity.  Here are a few examples:

The lower limit is 1

The upper limit is n


The lower limit is m

The upper limit is n


The lower limit is 1

The upper limit is infinity.


Example 1

Example 2

Some Manipulations