Mastering the MacLaurin Series and Radius of Convergence for f(x) = ln(1-x)

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Consider the function

f(x) = ln(1-x)

a) compute the MacLaurin series of f(x) (ie: the Taylor series of f(x) around x=0)

b) Compute the radius of convergence and determine the interval of convergence of the series in a)

c) Determine the Taylor series of f'(x) around x=0. Can you do so without using a)?

d) How would you have computed part a) if you had first done part c)?

Thank you!
 
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You need to show your work in order to get help. Forum guidelines.
 
Someone posted this exact same question in the Calculus and Analysis forum.
 

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