Finding the Taylor series of a function

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The discussion centers on the derivation of the Taylor series for a function, where a participant believes there is a mistake in the professor's factorization step after substituting x-1 with t. They specifically point out the omission of the term (-1)^(n+1) over 3^n, which they argue is necessary for the correct series representation. The participant expresses confidence in their assessment and concludes that their understanding is validated. The conversation emphasizes the importance of accuracy in mathematical derivations. Overall, the thread highlights the critical nature of factorization in finding Taylor series.
Amaelle
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Homework Statement
look at the image
Relevant Equations
taylor's series
Greetings!
1644257151464.png


Here is the solution that I understand very well I reach a point I think the Professor has mad a mistake , which I need to confirm

after putting x-1=t
we found:

1644257503194.png

But in this line I think there is error of factorization because we still need and (-1)^(n+1) over 3^n

Thank you!
Best regards!
 
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Thank you , I was right!

Best regards!
 

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