Series: Convergent or Divergent?

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The discussion centers on determining the convergence or divergence of the expression ln(2(n+1)) - ln(2n). A participant reformulates the expression to ln(1+(1/n)) but struggles to identify an appropriate comparison function (Bn) for the comparison test. Another contributor suggests examining the behavior of ln(1+x) as x approaches zero to assess convergence. The conversation emphasizes the importance of understanding logarithmic behavior in limit comparisons. Ultimately, the analysis aims to clarify whether the series converges or diverges based on these insights.
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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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