a) Find the Maclaurin series for the function f(x) = 1/1 + x b) Use differentiation of power series and the result of part a) to find theMaclaurin series for the function g(x) = 1/(x + 1)^2 c) Use differentiation of power series and the result of part b) to find theMaclaurin series for the function h(x) = 1/(x + 1)^3 d) Find the sum of the series ∞ SUM  n(n − 1)/(2n)n=3 This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is 7/2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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a) Find the Maclaurin series for the function


f(x) = 1/1 + x

b) Use differentiation of power series and the result of part a) to find the
Maclaurin series for the function

g(x) = 1/(x + 1)^2

c) Use differentiation of power series and the result of part b) to find the
Maclaurin series for the function

h(x) = 1/(x + 1)^3


d) Find the sum of the series

SUM  n(n − 1)/(2n)
n=3

This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is 7/2

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