WebQuestion: Find a power series for f (x)= 1/ (1-x)^3 Find a power series for f (x)= Show transcribed image text Expert Answer 100% (4 ratings) Transcribed image text: Find a power series for f (x)= 1/ (1-x)^3 Previous question Next question Get more help from Chegg Solve it with our Calculus problem solver and calculator. WebNov 30, 2016 · $\begingroup$ Thanks for the answer! This method is a little different than what we've learned. We're supposed to try and transform f(x) into the form 1/(1-r), where r < 1, and then recognize that Sum (r^n)...
Find a power series representation for this function
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Find power series representation for f (x) = 1/ (1+x).
WebYou can use the Rydberg equation to calculate the series limit of the Lyman series as a check on this figure: n 1 = 1 for the Lyman series, and n 2 = infinity for the series limit. … WebIn addition, we would like the first derivative of the power series to equal f ′ (a) at x = a. Differentiating Equation 6.4 term-by-term, we see that d dx ( ∞ ∑ n = 0cn(x − a)n) = c1 + 2c2(x − a) + 3c3(x − a)2 + ⋯. Therefore, at x = a, the derivative is d dx( ∞ ∑ n = 0cn(x − a)n) = c1 + 2c2(a − a) + 3c3(a − a)2 + ⋯ = c1. WebJun 22, 2024 · Calculus Power Series Introduction to Power Series 1 Answer Hammer Jun 22, 2024 1 (1 − x)2 = 1 + 2x + 3x2 + ... Explanation: We are given f (x) = 1 (1 − x)2 This is fairly similar to 1 1 − x, for which we know a power series: 1 1 − x = 1 + x + x2 +... = ∞ ∑ k=0xk The radius of convergence for this power series is x ∈ ( − 1,1). contemporary home lighting trends