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Examples ofconvergent series
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The right-hand side of the above equation is a uniformlyconvergentseriesof continuous functions.
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The summable families are absolutelyconvergentseries.
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Unfortunately the correspondingconvergentseriesconverges very slowly.
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This example is from Wikipedia and may be reused under a CC BY-SA license.With the norm in place, absolutelyconvergentseriescan be used instead of finite sums.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The simplest examples of conditionallyconvergentseries(including the one above) are the alternating series.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Or, possibly, due to theconvergentseries, human history might not change at all.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Analogously of course, the matrices whose row sums are absolutelyconvergentseriesalso form a ring.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The homotopy analysis method employs the concept of the homotopy from topology to generate aconvergentseriessolution for nonlinear systems.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The difference is that an asymptotic series can not be made to produce an answer as exact as desired, the way thatconvergentseriescan.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The method employs a homotopy transform to generate aconvergentseriessolution of differential equations.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The path formed by connecting the partial sums of a conditionallyconvergentseriesis infinitely long.
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This example is from Wikipedia and may be reused under a CC BY-SA license.One way to do this is by means of aconvergentseriesof inverted rising exponentials.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The arguments are ultimately justified for theseconvergentseries, implying that and, but the underlying proofs demand careful thinking about the interpretation of endless sums.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.