


$\begingroup$ The logarithm is a function, meaning that it has actually a well defined value for a offered $x$. Girlfriend can't leave an undetermined continuous in the meaning ! $\endgroup$
Because that is not true that us have$$\log(1+x)=x-\fracx^22+\fracx^33-\fracx^44+\cdots+C$$for an arbitrary consistent $C$. Since, once $x=0$, the LHS is $0$ and also RHS is $C$, $C=0$.
You are watching: Ln(1-x) power series

Since the original role is $\log (1+x)$ and for $x=0$ we have actually $\log (1+0)=0$ we require that likewise the collection is zero for $x=0$.

Thanks for contributing solution to urbanbreathnyc.comematics ridge Exchange!
Please be certain to answer the question. Carry out details and share her research!But avoid …
Asking for help, clarification, or responding to other answers.Making statements based on opinion; ago them increase with referrals or an individual experience.Use urbanbreathnyc.comJax to format equations. Urbanbreathnyc.comJax reference.
See more: What We Do In The Shadows Intro Song, What We Do In The Shadows Theme Song Lyrics
To learn more, view our tips on writing great answers.
article Your price Discard
By click “Post your Answer”, friend agree come our regards to service, privacy policy and also cookie policy
Not the prize you're looking for? Browse other questions tagged calculus logarithms power-series taylor-expansion or asking your very own question.

site design / logo design © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.9.24.40305
her privacy
By click “Accept all cookies”, girlfriend agree stack Exchange can store cookie on your maker and disclose information in accordance with our Cookie Policy.