Module 9 :  Infinite Series, Tests of Convergence,  Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture 27 :  Taylor and Maclaurin series [Section 27.2]
27.2.3 Theorem (Convergence of Taylor Series):
 

Let be an open interval and be a function having derivatives of all order in . For there exists a point between a and such that

       .

Further, the Taylor series of f at converges to if   

        .
  Proof
  Follows from theorem 14.1.1 we have already seen some examples of Taylor series expansion in section 14.1 we give some more examples.
   
 
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