Difference between revisions of "Arithmetico-geometric series"
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== Example Problems == | == Example Problems == | ||
* [[Mock_AIME_2_2006-2007/Problem_5 | Mock AIME 2 2006-2007 Problem 5]] | * [[Mock_AIME_2_2006-2007/Problem_5 | Mock AIME 2 2006-2007 Problem 5]] | ||
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+ | == See Also == | ||
+ | * [[Sequence]] | ||
+ | * [[Arithmetic sequence]] | ||
+ | * [[Geometric sequence]] |
Revision as of 12:08, 12 November 2006
An arithmetico-geometric series is the sum of consecutive terms in an arithmetico-geometric sequence defined as: , where and are the th terms of arithmetic and geometric sequences, respectively.
Contents
[hide]Finite Sum
The sum of the first n terms of an arithmetico-geometric sequence is , where is the common difference of and is the common ratio of . Or, , where is the sum of the first terms of .
Proof:
Let represent the sum of the first n terms.
Infinite Sum
The sum of an infinite arithmetico-geometric sequence is , where is the common difference of and is the common difference of (). Or, , where is the infinite sum of the .