Finding the Taylor series of a function

[Amaelle]

Homework Statement

look at the image

Relevant Equations

taylor's series

Greetings!

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:

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!

 

[Amaelle]

Thank you , I was right!

Best regards!