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The sum of k times the k th power of x is given analytically by .... Cao, J.-T. "A Method of Summing Series and Some Corollaries" [Chinese]. Math. Pract. ...
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mathworld.wolfram.com/PowerSum.html
mathworld.wolfram.com/PowerSum.html
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This particular technique will, of course, work only for this specific example, but the general method for finding a closed-form formula for a power series is to look for a way to obtain it (by differentiation, integration, etc.) from another power series whose sum is already known (such as the geometric series,
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www.math.toronto.edu/mathnet/questionCorner/powerseries...
www.math.toronto.edu/mathnet/questionCorner/powerseries.html
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English translation: a function of the sum of a power series ... 2) Conceivably, it could be a function given by the sum of two or more power series. There is no way to tell which is correct without context.
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www.proz.com/kudoz/2168450
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Please assist me with the attached problems, including: 8.7 Find the convergence set for the power series ... 8.8 Given the series (a) estimate the sum of the series by taking the sume of the first four terms. How accurate is. ... Twenty problems involving Power Series; Sum of Series; Estimate Using Terms;
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www.brainmass.com/homework-help/math/calculus/37433
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Interval of Convergence of a power series a. Consider the Power series sum of series from n=1 to infinity of FnX^n. Use the ratio test to determine the open interval on which the pwr series converges. b. Show that the Taylor. ... Power & Taylor Series of Fibonacci ... Taylor Series - Recall the Taylor series Sum(x^n/n!).
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www.brainmass.com/homework-help/math/calculus/10316
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Multimedia learning units on Power series - maths online Gallery ... The applet shows the graph of a function resulting from adding up the first 11 terms of a power series. The coefficients can be adjusted by means of scroll bars. Thus it is illustrated how the individual powers contribute to the sum.
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www.univie.ac.at/future.media/moe/galerie/potr/potr.htm...
www.univie.ac.at/future.media/moe/galerie/potr/potr.html
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Originally Posted by flybyme But if I use the ratio test, is a absolutely convergent sum also uniformly convergent? Originally Posted by flybyme As far as I understand it I can't use the ratio test to show uniform convergence. You certainl...
http://www.physicsforums.com/showthread.php?t=157839
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How can I calculate the sum of the power series x + 4x^2 + 9x^3 + 16x^4 + ... + n^2x^n + ...? ... Date: 02/10/2001 at 18:40:29 From: Ivan Subject: The sum of a power series Can you tell me how to calculate the sum of this power series? x + 4x^2 + 9x^3 + 16x^4 + ... + n^2x^n + ... |x|<1 I've found that the series...
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mathforum.org/library/drmath/view/56974.html
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