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|&gt;=1 4) The nth-term test shows that the series diverges ∑n=1∞4nn+1

Question

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|&amp;gt;=1 4) The nth-term test shows that the series diverges ∑n=1∞4nn+1

doplovif · Accepted Answer

The given series is ∑n=1∞4nn+1  Determine whether the series ∑n=1∞4nn+1 converges or diverges as follows.  The nth term test:  If the limit limn→∞an either does not exist or not equal to zero, then ∑n=1∞an diverges.  Find the limit limn→∞an as shown below.  limn→∞an=limn→∞4nn+1  limn→∞an=limn→∞4nn(1+1n)  limn→∞an=limn→∞4nnn(1+1n)  limn→∞an=limn→∞4nnlimn→∞n(1+1n)  ∞1  =∞  Since the limit limn→∞4nn+1 does not exist, the series ∑n=1∞4nn+1 diverges.  Hence, the nth term test shows that the series diverges.  Thus, the correct option is 4.

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

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

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New Questions in Calculus 2