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Power Series Representation

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(a) Find a power series representation for f(x) = ln(1+x). What is the radius of convergence?

(b) Use part (a) to find a power series for f(x) = x ln(1+x).

(c) Use part (a) to find a power series for f(x) = ln (x^(2)+1).

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Solution Summary

Three power series expansion problems are answered in detail.

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Please see the attached file.

(a) Find a power series representation for f(x) = ln(1+x). What is the radius of convergence?
Answer:
Let (1)
Let the power series expansion of f(x) be
(2)
Then ...

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