Find closed form of series SUM (nx)^(2n)

Thread starter Calculus!
Start date May 1, 2009
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Closed Form Series Sum

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The discussion focuses on finding a closed form for the series SUM (nx)^(2n) under the condition that |x| < 1. Participants suggest starting with the equation for the sum n*x^n, proposing to use integration or differentiation techniques to derive a solution. The series can be manipulated by relating it to known power series and applying calculus to simplify the expression. The goal is to express the series in a closed form function, enhancing understanding of its convergence and behavior. Ultimately, the discussion emphasizes the importance of mathematical manipulation in deriving closed forms for series.

May 1, 2009

Calculus!

If abs x < 1 find a closed form function (i.e. f(x) = x +1) for the following series:

\sum((nx)^(2n))

(reads: the series from n=1 to infinity of nx^(2n))

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May 1, 2009

eok20

Try to first find an equation for sum n*x^n = x*sum n*x^(n-1) using integration/differentiation.

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