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Lecture

MAT136H1 Lecture Notes - Antiderivative


Department
Mathematics
Course Code
MAT136H1
Professor
all

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11.9 Infinite Sequences & Series
Function Representation as Power Series
Question #4 (Medium): Radius of Convergence for Power Series From Indefinite Integral
Strategy
When the function
 has radius of R, then either
1)    
 
2)    

   


Also have the radius of convergence of .
Sample Question
Evaluate the indefinite integral as a power series. Then also determine the radius of convergence.


Solution
First taking the function inside the indefinite integral,   
  
 
 


Therefore, 
 


  

   


Since  converges for   which means the radius of convergence is  , also 
converges for   which also means the radius of convergence is   .
Therefore 
  

 also converges for   and has the radius of
convergence of   
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