Question
Asked Nov 25, 2019
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I am trying to find if this converges absolutly or conditionally, or diverges. I am not sure how to proceed when I get infinity/infinity. My steps are in the Image.

1. Determine if the series coverges or diverges. Where appropriate, specify if the convergence is absolute or condi-
tional. Be sure to justify your answers
Bamboo Paper
(1)"
Vn
(a)
CA
n=1
in(-y
lim
(-Y
n
nt
lim
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1. Determine if the series coverges or diverges. Where appropriate, specify if the convergence is absolute or condi- tional. Be sure to justify your answers Bamboo Paper (1)" Vn (a) CA n=1 in(-y lim (-Y n nt lim

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Expert Answer

Step 1

the series is absolutely convergent if ∑|an| is convergent.

The series is absolutely convergent if ∑|an| is divergent and ∑ an is convergent.

According to alternating convergence series, the series ∑ (-1)n bn converges if it satisfies,

  1. bn+1≤bn
  2. lim(n→∞) bn=0

According to p-series test, the series is converges if p>1 and diverges otherwise. Here general form of series is in the form,

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Step 2

Identify the function.

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(-1)" a

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Step 3

Check convergence for ∑ an using a...

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1 1 Vn+1 2.lim = 0

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