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posted by  prieto on 8/26/2008 11:40:12 PM  |  status: Live  

infinite sequences and series 9

Course Textbook Chapter Problem
N/A real analysis 4.1 9
Question Details:
Use theorem 4.1.6 to show that {sn} converges.
a)  (β0)
b)
c)  (r0)
d)
 
Theorem 4.1.6
(a) if {sn} is nondecreasing, then
(b) if {sn} is nonincreasing, then
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posted by VENUGOPAL on 8/27/2008 12:55:55 PM  |  status: Live
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Question:
Use theorem 4.1.6 to show that {sn} converges.
a)  (β0) =
CASE 1
α>β

THEN SERIES IS NON INCREASING.HENCE AS PER
Theorem 4.1.6
(a) if {sn} is nondecreasing, then ==S(1)=(1+α)/(1+β)...=FINITE VALUE
HENCE CONVERGENT
CASE 2
α<β
THEN SERIES IS NON DECREASING.HENCE AS PER
Theorem 4.1.6

(b) if {sn} is nonincreasing, then ==S(1)=(1+α)/(1+β)...=FINITE VALUE
HENCE CONVERGENT



b)

c)  (r0)
d)
 
Theorem 4.1.6
(a) if {sn} is nondecreasing, then
(b) if {sn} is nonincreasing, then

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