1. May 21, 2012 #1

   sid9221

   

   [tex] \sum_{1}^{\infty} (-1)^n(1+\frac{1}{n})^n [/tex]
   
   I've tried the alternating series test but the "b_n" part converges to e.
   
   Can't think of any other test...

    

   sid9221, May 21, 2012
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3. May 21, 2012 #2

   tiny-tim

   

   Science Advisor

   Homework Helper

   hi sid9221!
   
   hint: draw a_n against n on graph paper (as dots) …
   
   

   what does it look like? ​

    

   tiny-tim, May 21, 2012
4. May 21, 2012 #3

   sid9221

   

   I know I've seen the plot somewhere (can't remember the technical name).
   
   It looks like a sin function but one that's increasing .
   
   I know it diverges just can't prove it.

    

   sid9221, May 21, 2012
5. May 21, 2012 #4

   Mark44

   

   Insights Author

   Staff: Mentor

   Use the "n-th term test for divergence." If the limit of the n-th term in the series is different from 0 or doesn't exist, the series diverges.

    

   Mark44, May 21, 2012
6. May 21, 2012 #5

   sid9221

   

   How to you take the limit of (-1)^n.
   
   Wolfram alpha says e^2i 0 to Pi !?!!

    

   sid9221, May 21, 2012
7. May 21, 2012 #6

   Ray Vickson

   

   Science Advisor

   Homework Helper

   You are missing the whole point. If you have a series [itex] S = t_1 - t_2 + t_3 - t_4 + \cdots,[/itex] with all [itex] t_i > 0 \;( \text{or all } < 0),[/itex] you need [itex]|t_n| \rightarrow 0 [/itex] as [itex] n \rightarrow 0.[/itex] Of course the factors [itex] (-1)^n[/itex] do not have a limit, but that is not important.
   
   RGV

    

   Ray Vickson, May 21, 2012

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