Get solution: Using a Power Series In Exercises 1726, use the power series to determine

Chapter 9, Problem 22

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Using a Power Series In Exercises 17-26, use the power series

\(\frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^{n} x^{n}\)

to determine a power series, centered at 0, for the function. Identify the interval of convergence.

\(f(x)=\ln \left(1-x^{2}\right)=\int \frac{1}{1+x} d x-\int \frac{1}{1-x} d x\)

Text Transcription:

1 / 1 + x = sum_{n = 0}^{infty}(-1)^{n} x^n

f(x) = ln (1 - x^2) = int 1 / 1 + x dx - int 1 / 1 - x dx