Proving Divergence of Alternating Series with Limit Comparison Test

  • Thread starter Dell
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In summary, to prove a hypothesis, you must follow the scientific method which involves making an observation, forming a hypothesis, conducting experiments, analyzing data, and drawing a conclusion. To prove a mathematical theorem, you must use logical reasoning and mathematical principles, often by building upon previously established theorems, definitions, and axioms. Proving a scientific theory requires evidence from repeated experiments and observations that are reproducible and consistent with the predictions of the theory. Proving a historical event involves interpreting evidence and evaluating sources, using multiple perspectives and critical thinking skills. To prove a legal case, you must present evidence and arguments that support your position, such as witness testimony, documents, physical evidence, and expert opinions, with the burden of proof varying depending
  • #1
Dell
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how do i prove that the following series diverges?

[tex]\sum[/tex](-1)n-1*[tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex])

is it enough to say that

lim {n->inf} [tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex]) is not 0 ?


i know for regular series this would be okay but what about series with alternating signs??

how else can i tbe proven??
 
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  • #2
Yes, an alternating series converges if and only if the limit of the terms go to zero.
 
  • #3
thanks, youve really helped me with this work,
 

1. How to prove a hypothesis?

To prove a hypothesis, you must follow the scientific method. This involves making an observation, forming a hypothesis, conducting experiments, analyzing data, and drawing a conclusion.

2. How to prove a mathematical theorem?

To prove a mathematical theorem, you must use logical reasoning and mathematical principles. This may involve using previously established theorems, definitions, and axioms to build a logical argument.

3. How to prove a scientific theory?

To prove a scientific theory, you must have evidence from repeated experiments and observations that support the theory. This evidence should be reproducible and consistent with the predictions of the theory.

4. How to prove a historical event?

Proving a historical event can be challenging as it often involves interpreting evidence and evaluating sources. Historians use a combination of primary and secondary sources, critical thinking skills, and multiple perspectives to construct a plausible narrative of the event.

5. How to prove a legal case?

To prove a legal case, you must present evidence and arguments that support your position. This evidence can include witness testimony, documents, physical evidence, and expert opinions. The burden of proof varies depending on the type of case and jurisdiction.

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