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Find the Taylor series for $ f $ centered at 4 if

$ f^{(n)} (4) = \frac {(-1)^n n!}{3^n (n + 1)} $

What is the radius of convergence of the Taylor series?

$f(x)=\sum_{n=0}^{\infty} \frac{(-1)^{n}}{3^{n}(n+1)}(x-4)^{n}, \quad R=3$

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