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# 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.$f(x) = \ln (1 + x)$

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

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

to trouble me is finding McLaren Siri's or a flex, using the definition of a metal ore in Siri's also find their associate ID radius of commitments. So first, after zero is equal to zero. I promised we would one over one plus acts. Second derivative is the connective one over one plus X. It's Claire thirty. Derivative. It's connective. You two over one thanks the power of three for their return. Is it to read Negative green factorial over one plus thanks. There's a party for so we can find it. And definitive off is the call to Nick. You wanted the problem on minus one pounds on line one, cantorial over one class acts. It's a problem. So half and Cyril, it's called, too. Next wind problems in this one house, My spawn. Tara. So So my Clarence Siri's for After Max. This sum from zero to infinity half and they're all over nocturnal comes backs to end, which is equal to some from Syria from one to twenty. Thanks to end over in hams makes you want to the apartment and minus y thinks the limit cost too finicky, absolutely off. Look, you want Teo end over plus one, I'LL predict, who want to combine one pretend, which is a good one. So the greenness of origins, it's a good line.

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp