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- Find a power series representation for the function anddetermine the radius of convergence. f(x) = ln(5-x)Use the power series representation 1/(1 − x)= ∞ ∑ x3, |x| < 1 N=0 to find a power series representation of f(x) = x2/(4 + x). Include the interval of convergence in your answer.Calc & Anal Geometry II Use any appropriate series test to determine whether the series converges or diverges ∞ ∑ cos((2n+1)π/2 n=1
- state whether the series converges or diverges and by which convergence test. Options: a. diverges-alternating series test b. converges ratio test c. converges alternating series test d. diverges integral comparison test e. diverges ratio test f. diverges alternating series test ∞∑n=1 1 n10 ---------- 6 + n11 ∞∑n=1 4n ------ n10 ∞∑n=1 n2·4n ------- n!a) find the Maclaurin series for f(x)=ln(1+4x). b) Find the associated radius of convergence(a) Find a power series representation for the function.f(x)=2/(19+x) (b) Determine the interval of convergence.