Finding Values of p for Convergence: (-1)^(n-1)/ n^p

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SUMMARY

The convergence of the series defined by (-1)^(n-1) / n^p is determined by the value of p. For the series to converge, p must be greater than 1, aligning with the properties of p-series. The discussion clarifies that while the series has alternating terms, it is essential to recognize that it behaves like a p-series in terms of convergence criteria. The confusion regarding the series classification was addressed, emphasizing the need for clear communication in mathematical reasoning.

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  • Understanding of series convergence criteria
  • Familiarity with p-series and their properties
  • Basic knowledge of alternating series
  • Ability to analyze mathematical expressions and notation
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  • Study the properties of alternating series and the Alternating Series Test
  • Learn about the implications of the p-series test for convergence
  • Explore examples of series with varying p values to observe convergence behavior
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Homework Statement


For what values of p is the series con.
(-1)^ (n-1)/ (n)^(p)


Homework Equations



In order for a p series to converge, p should be greater than 1

The Attempt at a Solution



So an = 1/ n^p

and p > 1

Is that right ?
 
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You're making so many abbreviations and omissions that it's hard to tell what you're thinking -- I think you even confused yourself because of it. Try again, but this time say what you're doing, and why.
 
I don't think so,, the only abbreviation is Con. which means Convergent

** Am trying to find the valu of p for which the series will converge

What I thought about is : becauce it 's a p-series , then p should be P greater than 1 ?

What do you think ??
 
remaan said:
becauce it 's a p-series
No it's not.
 
So, give a hint? !
 
Oh, you I mean this part is a p- series, the one I considered as an
 

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