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Lecture 27

MATH 2B Lecture 27: Representations of Functions as Power SeriesPremium


Department
Mathematics
Course Code
MATH 2B
Professor
ERJAEE, G.
Lecture
27

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03/08/2019
MATH 2B - Lecture 27 - Representations of Functions as Power Series
We first recall the geometric series
      
Expanding it, we obtain
   

Therefore, we can shift the index n by 1, and obtain a new form for geometric series
     
Now, we consider a simple power series

    
We can treat this power series as a geometric series by letting    
Similarly, we have

      
Therefore, we can think this power series as a function. But this only hold on a
certain interval

So, a power series is equal to a function only on its interval of convergence
Now, we try to represent some functions by using power series, and we also
need to find the interval of convergence
Example:
Represent
 by power series
Solution:
We always need the geometric series
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