Unformatted text preview: ∑ kx n does have its attractions: it appears to be an inﬁnite version of one of the simplest function types—a polynomial. This leads naturally to the questions: Do other functions have representations as series? Is there an advantage to viewing them in this way? The geometric series has a special feature that makes it unlike a typical polynomial— the coeﬃcients of the powers of x are the same, namely k . We will need to allow more general coeﬃcients if we are to get anything other than the geometric series. DEFINITION 10.43 A power series has the form ∞ X n =0 a n x n ,...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Power Series, Compute lim, kxn, Compute lim an

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