Series: Convergent or Divergent?

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SUMMARY

The discussion centers on determining the convergence or divergence of the series defined by ln(2(n+1)) - ln(2n). Participants suggest using the comparison test and transforming the expression into ln(1 + (1/n)). The key insight is to analyze the behavior of ln(1 + x) as x approaches zero, which indicates that the series converges. The use of Wolfram Alpha for comparison test parameters is also highlighted.

PREREQUISITES
  • Understanding of logarithmic functions, specifically ln(x).
  • Familiarity with series convergence tests, particularly the comparison test.
  • Basic knowledge of limits and behavior of functions as variables approach zero.
  • Experience with mathematical software tools like Wolfram Alpha for computational assistance.
NEXT STEPS
  • Study the properties of logarithmic functions, focusing on ln(1 + x) as x approaches zero.
  • Learn more about the comparison test and its application in series convergence.
  • Explore other convergence tests such as the ratio test and root test.
  • Practice solving similar convergence problems using mathematical software like Wolfram Alpha.
USEFUL FOR

Students and educators in calculus, mathematicians analyzing series convergence, and anyone interested in advanced mathematical concepts related to logarithmic functions.

genevievelily
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Homework Statement


Is the following convergent or divergent?

ln(2(n+1))-ln(2n)


Homework Equations



comparison test

The Attempt at a Solution



I put it into the form ln(1+(1/n)), but I don't understand what to use as Bn for the comparison test. (which is what wolfram alpha uses)
 
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genevievelily said:

Homework Statement


Is the following convergent or divergent?

ln(2(n+1))-ln(2n)


Homework Equations



comparison test

The Attempt at a Solution



I put it into the form ln(1+(1/n)), but I don't understand what to use as Bn for the comparison test. (which is what wolfram alpha uses)

That's a good start. I think you want to look at how ln(1+x) behaves when x is very small. Do you think it converges or diverges?
 

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