Working with binomial series Use properties of

Chapter 8, Problem 44E

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QUESTION:

Working with binomial series Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. Use the Taylor series

\((1+x)^{-2}=1-2 x+3 x^{2}-4 x^{3}+\cdots\),    for -1 < x < 1.

\(\left(x^{2}-4 x+5\right)^{-2}\)

Questions & Answers

QUESTION:

Working with binomial series Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. Use the Taylor series

\((1+x)^{-2}=1-2 x+3 x^{2}-4 x^{3}+\cdots\),    for -1 < x < 1.

\(\left(x^{2}-4 x+5\right)^{-2}\)

ANSWER:

Solution 44EStep 1:In this problem we need to find the first four nonzero terms of the Taylor series centered a

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