Does the series (showing the picture) converge or diverge? Choose the correct answer below. 1) The integral test shows that the series converges 2) Th

opatovaL 2021-01-16 Answered

Does the series (showing the picture) converge or diverge?
Choose the correct answer below.
1) The integral test shows that the series converges
2) The nth-term test shows that the series converges
3) The series diverges because the series is a geometric series with |r|>=1
4) The nth-term test shows that the series diverges
n=14nn+1

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Expert Answer

doplovif
Answered 2021-01-17 Author has 71 answers
The given series is n=14nn+1
Determine whether the series n=14nn+1 converges or diverges as follows.
The nth term test:
If the limit limnan either does not exist or not equal to zero, then n=1an diverges.
Find the limit limnan as shown below.
limnan=limn4nn+1
limnan=limn4nn(1+1n)
limnan=limn4nnn(1+1n)
limnan=limn4nnlimnn(1+1n)
1
=
Since the limit limn4nn+1 does not exist, the series n=14nn+1 diverges.
Hence, the nth term test shows that the series diverges.
Thus, the correct option is 4.
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Jeffrey Jordon
Answered 2021-12-16 Author has 2087 answers

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