58) Which of the following statements are true? a) The integral dx converges. b) The seriesE)" converges. n=1 c) The series (In(n))In(n) COnverges. n=5 d) The integral Tntel dx converges. (In(z))ln(=) (In(n))In(In(r)) n=5
58) Which of the following statements are true? a) The integral dx converges. b) The seriesE)" converges. n=1 c) The series (In(n))In(n) COnverges. n=5 d) The integral Tntel dx converges. (In(z))ln(=) (In(n))In(In(r)) n=5
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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Question
Solve both 58 and 59 please
![58) Which of the following statements are true?
a) The integral dx converges.
b) The series E)" converges.
n=1
c) The series Tnim converges.
(In(n))In(7)
n=5
d) The integral Intala dx converges.
(In(r))ln(=)
e) The series E
(In(n))In(In(n))
(In(n)) Converges.
n=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09caa562-c0c8-4a11-85df-abb5e549e1a9%2F5a46b6e0-6e3a-4660-9b91-2ae6365bc3e4%2Fwjcxwf_processed.png&w=3840&q=75)
Transcribed Image Text:58) Which of the following statements are true?
a) The integral dx converges.
b) The series E)" converges.
n=1
c) The series Tnim converges.
(In(n))In(7)
n=5
d) The integral Intala dx converges.
(In(r))ln(=)
e) The series E
(In(n))In(In(n))
(In(n)) Converges.
n=
![59) Assume that an > 0 for all n e N and an+1 < an for all n > 100. Consider the
series
an
n=1
k
with k-th partial sum Sk = E(-1)"+1an.
n=1
Which of the following statements are true?
a) The series converges if and only if lim an = 0.
= 0.
n00
b) If E(-1)"+'a, converges to S, then S12 < S < S13.
n=1
c) If E(-1)"+l an converges to S, then S234 < S < S235.
n=1
d) If E(-1)"+an converges to S, then |S – S45| < a46-
n=1
e) If E(-1)"+'am converges to S, then |S – S239| < a240-
n=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09caa562-c0c8-4a11-85df-abb5e549e1a9%2F5a46b6e0-6e3a-4660-9b91-2ae6365bc3e4%2Fi8fs3c3_processed.png&w=3840&q=75)
Transcribed Image Text:59) Assume that an > 0 for all n e N and an+1 < an for all n > 100. Consider the
series
an
n=1
k
with k-th partial sum Sk = E(-1)"+1an.
n=1
Which of the following statements are true?
a) The series converges if and only if lim an = 0.
= 0.
n00
b) If E(-1)"+'a, converges to S, then S12 < S < S13.
n=1
c) If E(-1)"+l an converges to S, then S234 < S < S235.
n=1
d) If E(-1)"+an converges to S, then |S – S45| < a46-
n=1
e) If E(-1)"+'am converges to S, then |S – S239| < a240-
n=1
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