Unformatted text preview: A power series centered at a has the form ∞ X n =0 a n ( xa ) n , with the understanding that a n may depend on n but not on x . Exercises Find the radius and interval of convergence for each series. 1. ∞ X n =0 nx n ⇒ 2. ∞ X n =0 x n n ! ⇒ 3. ∞ X n =1 n ! n n x n ⇒ 4. ∞ X n =1 n ! n n ( x2) n ⇒ 5. ∞ X n =1 ( n !) 2 n n ( x2) n ⇒ 6. ∞ X n =1 ( x + 5) n n ( n + 1) ⇒ 10.9 Calculus with Power Series Now we know that some functions can be expressed as power series, which look like inﬁnite polynomials. Since calculus, that is, computation of derivatives and antiderivatives, is easy...
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 Fall '07
 JonathanRogawski
 Math, Calculus, Geometric Series, Power Series

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