Question
Asked Oct 19, 2019

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...

Let
1
1+ (2x)+ (2x) +.+(2x)"
1-2x
f(x)=
the power series exp ansion (geometric series,
valid for |2x<1,i.e, x|< 0.5
so, radius of convergence = 0.5
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Let 1 1+ (2x)+ (2x) +.+(2x)" 1-2x f(x)= the power series exp ansion (geometric series, valid for |2x<1,i.e, x|< 0.5 so, radius of convergence = 0.5

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Math

Calculus