3. ( for ) Find the power series representation f(x) = Σen(x - a)" n=0 f(x) = = 1 about x=a=0. Also determine the Interval of Convergence of the series. Hint: You may use the result from Geometric Series: X X 1+x5 = Σx", |x| < 1 n=0

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A: To find the convergence, we will use ratio test. D' Alembert's Ratio test: Consider the series ∑nan…

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Q: 3. Find the interval of convergence of the series ☎ n=1 (-1)"+¹(x-2)" 3"-n

A: Find the interval of convergence of the series

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Q: (b) (a) -5 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c) s²L(y(x))-sy(0) - y'(0) b) s² L(y(x)) + sy(0)…

A: We have to find the correct choice.

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Q: Find the radius and interval of convergence for the following series: (x - 2)" 10" a. 8 n=0 Radius=…

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A: Given apply ratio test

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Q: Find an easy expression for the sum of the series on its interval of convergence. (-1)"-'n -x" 2"…

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A: We can answer first question as per the honor policy. Please resubmit the other question as well to…

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Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

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