Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 25RE: Use the formula for the sum of the first nterms of a geometric series to find S9 , for the series...
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1. B using ratio tes
Transcribed Image Text:2
PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.10
1. Find the radius of convergence and interval of convergence of the power series.
1
TD
12"
an= (x+3)
ant) - (x+2) • 4²
(n+1) ₂2 (1+1)
an (ntl)
(a)
(b)
(c)
(d)
M8 M8 IM8 IM8 IM
1
n2n
(e) Σ
n=0
n²2
22-1-1 (0*-
n!
(x+2)²²a=2
lim | 01/2+1/1 = 1 m 2 (171) √x+2) = 1/2 -4x+2) =
호 금
1/2 - 1/x+²2) = 12x+1²1 1/2 x=2 x=1
(3x - 1)"
(x-3)"
(n+1)"
3n
1
2n+1
-xn
-(x-1) 2n
2. Find the Taylor series of the function f(x) at the point a.
(a) f(x) = ²x, a=1
1
(b) f(x) =
1-x
(c) f(x) = lnx,
3. Find the Maclaurin series of the function f(x).
a=2
(x+2) ++^)
(x+2ja (^+1)=2
n
a=3
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