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Real Analysis : Power Series - Expansion and Interval of Convergence

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Let ...

a) Show that f can be represented by a power series. What is its interval of convergence?

b) Calculate the power series expansion for the function F(x) = ...

Please see attached for equations.

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(a) Since ,which is a power series, then
if , therefore
f(x)= , since if x=0, f(0)=1, and if , f(x) ...

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