(d) n=2 COS() For each of the following series decide if it is Absolutely Convergent, Conditionally Convergent, or Divergent. You must justify all answers. ∞ n (e) (-1) 3n+2n+7 (f) n=1 iM8 n=1 5n8-4n2 11+3sin(n) 2n-1 h=2 COS() 11+3sin(n) 11±3 F ~ 2n-1 2n-1 2n Diverges as a n=1 P-series. DCT. 11+3sin(n) NTS 2n-1 2n TED Tim n1-390 = Cos() Cos()=1+0. So this series Diverges by TED Proof 11 +35in(n) Since 2 2n-1 nce & Diverges Series 2n x11+3sin(n) 2n-1 h=1 8 20 as a p-series by DCT also diverges ทะเ (-1)" 344 +2n+7 558-452 Consider Elanl Root Test. lim n-78 /n Tim n-700 3n4+2n+7 518-452 17m 3n4+2n+7 1/48 5-4n2 408 1-700 Tim 9720 = 13/140 2/123047/483 5-4/4670 -12-1. <1 = A.C. く So by Root Test This series A. C
(d) n=2 COS() For each of the following series decide if it is Absolutely Convergent, Conditionally Convergent, or Divergent. You must justify all answers. ∞ n (e) (-1) 3n+2n+7 (f) n=1 iM8 n=1 5n8-4n2 11+3sin(n) 2n-1 h=2 COS() 11+3sin(n) 11±3 F ~ 2n-1 2n-1 2n Diverges as a n=1 P-series. DCT. 11+3sin(n) NTS 2n-1 2n TED Tim n1-390 = Cos() Cos()=1+0. So this series Diverges by TED Proof 11 +35in(n) Since 2 2n-1 nce & Diverges Series 2n x11+3sin(n) 2n-1 h=1 8 20 as a p-series by DCT also diverges ทะเ (-1)" 344 +2n+7 558-452 Consider Elanl Root Test. lim n-78 /n Tim n-700 3n4+2n+7 518-452 17m 3n4+2n+7 1/48 5-4n2 408 1-700 Tim 9720 = 13/140 2/123047/483 5-4/4670 -12-1. <1 = A.C. く So by Root Test This series A. C
Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Transcribed Image Text:(d)
n=2
COS()
For each of the following series decide if it is
Absolutely Convergent, Conditionally
Convergent, or
Divergent. You must justify all answers.
∞
n
(e) (-1) 3n+2n+7
(f)
n=1
iM8
n=1
5n8-4n2
11+3sin(n)
2n-1
h=2
COS()
11+3sin(n)
11±3
F
~
2n-1
2n-1
2n
Diverges
as a
n=1
P-series.
DCT.
11+3sin(n)
NTS
2n-1
2n
TED
Tim
n1-390
=
Cos()
Cos()=1+0.
So this series Diverges
by TED
Proof 11 +35in(n)
Since 2
2n-1
nce & Diverges
Series
2n
x11+3sin(n)
2n-1
h=1
8
20
as
a p-series by DCT
also diverges
ทะเ
(-1)"
344 +2n+7
558-452
Consider Elanl
Root Test.
lim
n-78
/n
Tim
n-700
3n4+2n+7
518-452
17m
3n4+2n+7
1/48
5-4n2
408
1-700
Tim
9720
=
13/140 2/123047/483
5-4/4670
-12-1. <1 = A.C.
く
So by Root Test
This series
A. C
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