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Power series from the geometric series Use the

Chapter 1, Problem 25RE

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QUESTION:

Use the geometric series \(\sum _{k=0}^{\infty}\ x^k=\frac{1}{1-x}\), for |x| < 1 to determine the Maclaurin series and the interval of convergence for the following functions.

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

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QUESTION:

Use the geometric series \(\sum _{k=0}^{\infty}\ x^k=\frac{1}{1-x}\), for |x| < 1 to determine the Maclaurin series and the interval of convergence for the following functions.

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

ANSWER:

Solution 25RE

Step 1:

In this problem we have to use the geometric series for |x|<1, to determine the Maclaurin series of and also we have to find the interval of convergence

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