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How to prove the following:

  • Thread starter Dell
  • Start date
  • #1
590
0
how do i prove that the following series diverges?

[tex]\sum[/tex](-1)n-1*[tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex])

is it enough to say that

lim {n->inf} [tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex]) is not 0 ???


i know for regular series this would be okay but what about series with alternating signs??

how else can i tbe proven??
 

Answers and Replies

  • #2
1,838
7
Yes, an alternating series converges if and only if the limit of the terms go to zero.
 
  • #3
590
0
thanks, youve really helped me with this work,
 

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