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Using the Constant Multiple Rule for Simplifying a Series

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Updated:  
2016-03-26 18:17:21
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From The Book:  
Calculus II Workbook For Dummies
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The Constant Multiple Rule for integration allows you to simplify an integral by factoring out a constant. This option is also available when you’re working with series. Here’s the rule:

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For example:

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To see why this rule works, first expand the series so you can see what you’re working with:

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Working with the expanded form, you can factor a 7 from each term:

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Now express the contents of the parentheses in sigma notation:

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As if by magic, this procedure demonstrates that the two sigma expressions are equal. Of course, this magic is really nothing more exotic than your old friend from grade school, the distributive property.

About This Article

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About the book author:

Mark Zegarelli is a math tutor and author of several books, including Basic Math & Pre-Algebra For Dummies.