Question
Asked Nov 20, 2019
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Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.
CO
(-1)"
In(4n)
Σ
n=2
O absolutely convergent
conditionally convergent
divergent
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Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent. CO (-1)" In(4n) Σ n=2 O absolutely convergent conditionally convergent divergent

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Expert Answer

Step 1

Consider the given series.

Use the alternating series, the definition of conditionally convergent seri...

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It is known that a seriesa, is called conditionally convergent when it is convergent but not absolutely convergent. It is also known that if the alternating series E-) b bb,-b,+b,-bb>0 satisfies b b, for all n and limb 0, then the series is convergent (1)" In (4n) Given (-1)" 1 Consider (-) and b In (4n) In (4m) 2 1 Also b n n 0 for n2 2. For all n2 2, n+1>n 1 In(n 1 n n 1 = 0 In(4n Therefore, b is decreasing for nz 2 and limb, limb

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