geometric series
1
7.2
- noun
- /dʒiˈɑːmɛtrɪk ˈsɪriz/
- Specialized
:
serie geométrica
- When the common ratio of a geometric series is less than one, the sum converges to a finite value.
Two to the log N this is a geometric series.
- Two to the log N this is a geometric series.
Examples
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First, if the common ratio R of a geometric series has absolute value less than one, the series has a finite total.
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Suppose the MFLOP rate were constant at each level; then the computation time would follow a geometric series with ratio r = 1/4.
Academic text (1997) -
What makes it a geometric series is this value here of R, which is the constant multiple, right?
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And now we have a usual infinite geometric series, and we have a formula for this.
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It's a convergent geometric series, so converges by the geometric series test.
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This is clearly an infinite geometric series that will converge to 1/(1 - Alpha Gamma) provided that Alpha Gamma < 1.
Academic text (1999) -
A geometric series is defined by the formula, where each term after the first is found by multiplying by the constant ratio R.
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The value of each term in a geometric series can be calculated by multiplying the previous term by a fixed constant.
Surface Forms
Morphology
The compound clearly denotes a specific kind of mathematical series, so there is a partial connection to the constituents ('geometric' + 'series'). However, the crucial property — that successive terms are related by a constant multiplicative ratio — is a technical detail not predictable from the everyday meanings of the words, so a B1 learner knowing the constituents would likely not infer the full definition without math knowledge.
Etymology
The term geometric series comes from a simple picture: a series (a list) of numbers where each next number is made by multiplying the one before by the same 'ratio'. Imagine boxes that get half as big each time or money that grows by the same percent; that image shows why the term means a list built by repeating the same multiplication.