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Numerade Educator

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Problem 15 Easy Difficulty

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence.

$ f(x) = 2^x $

Answer

$f(x)=\sum_{n=0}^{\infty} \frac{(\ln 2)^{n} x^{n}}{n !} ,\quad R=\infty$

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Video Transcript

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