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Unformatted text preview: e convergence at endpoints But then Example 1: ﬁnd the radius of
convergence of the power series
4 n (−4)
n+3 (n + 1) + 3
∞ an xn Solution: this is a power series
with n=0 R = lim n→∞ an
an = √
= (−1)n √
n+3 ∞ an xn be a general To begin to understand what the Radius of convergence does for us, let
power series. Whenever the series converges it deﬁnes a function n=0 ∞ an xn . f (x) = a0 + a1 x + a2 x2 + a3 x3 + . . . + an xn + . . . =
n=0 It’s certainly deﬁned at x = 0, for instance, since f (0) = a0 . Deﬁnition: the Interval of Convergence of a power series n an xn is the largest interval on which the series is deﬁned; it is the domain of
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This note was uploaded on 06/05/2011 for the course MATH 408 D taught by Professor Gilbert during the Spring '11 term at University of Texas at Austin.
- Spring '11
- Power Series