Finding the Taylor series of a function

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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!