Functions to power series Find power series

Chapter 8, Problem 39E

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QUESTION:

Functions to power series Find power series representations centered at 0 for the following functions using known power series. Give the interval of convergence for the resulting series.

\(f(x)=\frac{1}{1+x^{2}}\)

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QUESTION:

Functions to power series Find power series representations centered at 0 for the following functions using known power series. Give the interval of convergence for the resulting series.

\(f(x)=\frac{1}{1+x^{2}}\)

ANSWER:

Solution 39E

Step 1:

We know the power series of the geometric series  is

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