(-1)"4"+1,n+1 3n+1(n +1) In this problem, we investigate the power series n=0 (a) Show that 5-1)"4"+1µn+1 3n+1(n + 1) 4.x is the Taylor series for the function f(x) = In 3 centred on I = 0. 4x (b) For which values of r is the series equal to In 3

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A: Since you have posted multiple questions. I am answering the first one. Please post the question…

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Q: Given: In(1 + x) =(-1)". - xn+1 if |x| < 1. n +1 n=0 Find the Maclaurin series for f(x) = x ln (1…

A: Here given that: ln(1+x)=∑n=0∞(-1)nn+1xn+1  ...(1)if |x|&lt;1

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Q: Eo(-1)" = 1 + (-1) + 1 + (-1) + --- = (1 – 1) + (1 – 1) + --- = 0 + 0 +.. = 0 ... %3D True False

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Q: (-1)"4"+1,n+1 3n+1(n + 1) In this problem, we investigate the power series n=0 Σ (-1)"4"+lpn+1…

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Q: (4) Σ n=2 3n η3 x 5m (4)

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Q: (s) If the Taylor series of a function f (x) is 2n(n + 1) n=1 (a) identify Cn- (b) find f(4) (0).

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Q: page 6 6. (a) Find a simplified power series representation (in terms of x") for g(x) and determine…

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