Use the power series 1+x (-1)^yn, Ix| < 1 1 + x n = 0 to find a power series for the function, centered at 0. 1 g(x) : x2 + 1 g(x) = n= 0 Determine the interval of convergence. (Enter your answer using interval notation.)

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A: according to the given problem, we have

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A: According to the guidelines, the first 3 questions will be answered.

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A: soln: step1: write a fx as a power series centered at c=-1fx=22-xwe know general formula power…

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Q: solve the problem by use the hint

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A: Given 11+x = ∑n=0∞(-1)nxn = 1 - x + x2 - x3 + ...

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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