+00 +00 (a) Suppose that 2 an and 2 b, are series with positive terms n=1 n=1 +oo an and that > b, is convergent. Prove that if lim n→+∞ b, %3D n=1 +0o then a, is also convergent. n=1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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This is a two-part problem regarding comparison tests for infinite series. 

+oo
+oo
- (a) Suppose that > an and 2 b, are series with positive terms
n=1
n=1
and that > b, is convergent. Prove that if
lim
n→+∞ b.
n
n=1
then a, is also convergent.
n=1
(b) Use part (a) to show that the series converges.
+o0
In (n)
(1) E
In (n)
(ii) E
n=1 Vn · en
n3
n=1
||
Transcribed Image Text:+oo +oo - (a) Suppose that > an and 2 b, are series with positive terms n=1 n=1 and that > b, is convergent. Prove that if lim n→+∞ b. n n=1 then a, is also convergent. n=1 (b) Use part (a) to show that the series converges. +o0 In (n) (1) E In (n) (ii) E n=1 Vn · en n3 n=1 ||
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