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Social ScienceUse any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.CO(-1)"In(4n)Σn=2O absolutely convergentconditionally convergentdivergent
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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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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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