11 дек. 2008 г. · The power series representation for x/(1-x)^2 is x + 2x^2 + 3x^3 + 4x^4 + ... when centered on 0. This can be obtained by using the Taylor series expansion. |
18 мар. 2009 г. · The power series representation for 1/(1+x^2) is 1 - x^2 + x^4 - x^6 + ... + (-1)^n * x^(2n) + ... on the interval (-1,1). |
7 дек. 2004 г. · In summary, A power series expansion is a mathematical representation of a function as an infinite sum of powers of a variable. |
28 нояб. 2011 г. · The power series representation of xln(1+x^2) is ∑n=0∞ ((-1)^n * x^(2n+1))/(2n+1), where n is a non-negative integer. |
27 окт. 2012 г. · Homework Statement. I am asked to find a power series for the function f(x) = 2/(1 - x^2), centered at 0. |
17 апр. 2017 г. · In summary, the conversation discusses how to show that 1 1 + x 2 = 1 x 2 − 1 x 4 + 1 x 6 − 1 x 8 + ⋯ by using power series expansion. |
30 июн. 2014 г. · The Maclaurin Series for f(x)=(1-x)^-2 is 1 + 2x + 3x^2 + 4x^3 + ..., which can also be written as the summation notation ∑ n=0 to ∞ (n+1)x |
6 янв. 2016 г. · The Taylor series for 1/x here is centered at 1, which means that the Taylor series will be in powers of (x - 1). The same will be true of the series for 1/x 2. |
4 дек. 2012 г. · The Maclaurin series for (1-x)^-2 has a radius of convergence of 1, meaning it converges for all values of x within a distance of 1 from the ... |
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