  # Find the power series representation for g centered at 0 by differentiating or integrating the power series for f(perhaps more than once). Give the interval of convergence for the resulting series. g(x) = ln(1 - 2x) using f(x) = 1/1 - 2x.

Question

Find the power series representation for g centered at 0 by differentiating or integrating the power series for f(perhaps more than once). Give the interval of convergence for the resulting series. g(x) = ln(1 - 2x) using f(x) = 1/1 - 2x.

check_circleExpert Solution
Step 1

To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence

Step 2

The power series for f(x) is just the geometric series derived fro...

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### Calculus 