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Find the Taylor series for $ f(x) $ centered at the given value of $ a. $ [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) = e^{2x},$ $ a = 3 $

$=\sum_{0}^{\infty} \frac{(x-3)^{n} \cdot e^{6}}{n !} \cdot 2^{n}$

Radius$=\infty$

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