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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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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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The problem is finding that Tiller Siri's for half centered at war. If and stare. It'd off off to the point actually good before and say hello to makes you want to end house the factorial over three to end house in past lives so fast. Commoners half in a Siri's centered at Or that's the control, some from zero to infinity, half conservative point for over. In fact, Arial Towns X minus four to the public. This is a call to some from zero to infinity. Toby used its result. Nick. You want to end over three to end Paswan X months for to the problem. Yeah, what is the readers of convergence of the groceries? Face the limit. Industrial serenity like you want to impress one over the range, plus one hands from class, too over next to want and over Great and passed on. This is a cultural event and goes to Vanity one over Green to Plus one casts a prostitute. Comes three two incomes plus one over one. So this is the culture limit goes to infinity and plus one over three times plus two, which is the control my food, says the readers of comedians. Is it all true? One over run over three synthesis equal to three. The res of emergence of groceries is three.

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp