Unformatted text preview: k th derivative: k !(1x )k1 = ∞ X n = k n ! ( nk )! a n ( x + 2) nk and substituting x =2 we get k !3k1 = k ! a k and a k = 3k1 = 1 / 3 k +1 , so the series is ∞ X n =0 ( x + 2) n 3 n +1 . We’ve already seen this, on page 261 . Such a series is called the Taylor series for the function, and the general term has the form f ( n ) ( a ) n ! ( xa ) n . A Maclaurin series is simply a Taylor series with a = 0....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Maclaurin Series, Taylor Series, Sequences And Series

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