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Convergence - Divergence of a Series

  • Thread starter remaan
  • Start date
  • #1
132
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Homework Statement


Test the series for convergence or divergence
-1/3+ 2/4 - 3/5 +4/6 - 5/7 + .................


Homework Equations



I think it's an alternating series

The Attempt at a Solution



I found that an = (-1) ^n * n/ (n+2)

And it approaches 1 as n goes to inifty so the series will Diverge

Is that right ??
 

Answers and Replies

  • #2
1,444
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hmmm.
alternating series test says that if you can identify a series of the form [itex]\sum (-1)^n a_n[/itex] and the [itex]a_n[/itex] are positive and decreasing such that [itex]a_n \rightarrow 0[/itex] then [itex]\sum (-1)^n a_n[/itex] will converge.

so here you have [itex]a_n=\frac{n}{n+2}=\frac{1}{1+\frac{2}{n}}[/itex]

how does this behave as [itex]n \rightarrow \infty[/itex]
 
  • #3
132
0
It will approach 1. and the series will Diverge.

What do you think ?
 

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