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What is the power series representation of ln(1-2x)? What is its radius of convergence?

What is the power series representation of ln(1-2x)?

What is its radius of convergence?

Expert Solution

PART(a): To find the power series

The given function is,

we have the following power series,

put u = -2x,

PART(b): To find the radius of convergence

The given nth term is,

The Ratio Test is given by,

divide by n,

plugin the limit,

For the radius of convergence,

The above inequality can be compared with,

where R is the radius of convergence given by,

I hope this answer helps,
Thanks,
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milcah answered 2 years ago

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