Handwritten only asap 1. Test the convergence of the power series below:(1 - 2n)³(-4)"n=1Calculate the following:a. Center of convergenceb. Radius of convergencec. interval of convergence-(x-3)"2. Express as a single power series form:DOΣ(n − 2)an+1(2x − 3)+¹ + Σan-1(2x − 3)²-1n=0n=23. For the function y = x ln(x + 1), determine itsa. MacLaurin Series expansion up to fifth degree.b. Taylor Series expansion up to fifth degree at xo = 2.4. Test the point and find the solution to the differential equation below:y" + x²y' + xy = 0 at x₁ = 05. Find the solution to the differential equations below:a. 3x²y" + 6xy' + y = 0b. x²y" + 3xy' = 0, given y(1) = 0, y' (1) = 4

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College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.4: Series And Their Notations

Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+

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1. Test the convergence of the power series below: (1 - 2n)³ (-4)" n=1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence -(x-3)"