Finding the Taylor series of a function

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SUMMARY

The discussion focuses on finding the Taylor series of a function, specifically addressing a potential error in factorization related to the term (-1)^(n+1) over 3^n. The user expresses confidence in their understanding and highlights a mistake made by the professor in the derivation process. This indicates a critical examination of the Taylor series expansion and its components.

PREREQUISITES
  • Understanding of Taylor series and their derivation
  • Familiarity with factorization techniques in algebra
  • Basic knowledge of mathematical notation and sequences
  • Experience with calculus concepts, particularly series expansions
NEXT STEPS
  • Study the derivation of Taylor series for various functions
  • Learn about common errors in factorization and how to avoid them
  • Explore the implications of alternating series in Taylor expansions
  • Review examples of Taylor series applications in real-world problems
USEFUL FOR

Students of calculus, mathematics educators, and anyone involved in mathematical analysis or series expansions will benefit from this discussion.

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!
 
Physics news on Phys.org
Thank you , I was right!

Best regards!
 

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