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Sum of an Infinite Geometric Series
When an infinite geometric series is convergent (that is, when ), its sum can be computed using the formula:
where is the first term and is the common ratio. This formula is derived from the partial-sum formula . Because , the term approaches zero as grows infinitely large. Replacing with in the partial-sum formula gives . Notice that is written without the subscript because the sum is not limited to a finite number of terms. This formula applies only when the series is convergent; when , the series is divergent and no finite sum exists.
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Divergent Infinite Geometric Series
Convergent Infinite Geometric Series
Sum of an Infinite Geometric Series
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Example: The Multiplier Effect as an Infinite Geometric Series
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Formula for the Sum of an Infinite Geometric Series
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