Suppose g has a power series representation at –2 and g(7) is the n-th derivative of g. If g(x) = On (x + 2)" for all æ, then O a. the power series must diverge. O b. the radius of convergence is ∞ O c. g(m) (2) п! d. g(m)(-2) n! e. the interval of convergence is (-x, a) O f. b, = 1! O g. bz = 3!

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Suppose g has a power series representation at -2 and g(m) is the n-th derivative of g. If g(x) = bn (x + 2)²
for all æ, then
a. the power series must diverge.
O b. the radius of convergence is ∞
g(") (2)
bn
n!
Od.
g(m)(-2)
n!
O e.
the interval of convergence is (-0, 0)
O f. b = 1!
O g. bz = 3!
Transcribed Image Text:00 Suppose g has a power series representation at -2 and g(m) is the n-th derivative of g. If g(x) = bn (x + 2)² for all æ, then a. the power series must diverge. O b. the radius of convergence is ∞ g(") (2) bn n! Od. g(m)(-2) n! O e. the interval of convergence is (-0, 0) O f. b = 1! O g. bz = 3!
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