Give an example of such a convergent series

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Homework Statement



Give an example of a convergent series [tex]\Sigma[/tex] z[tex]_{n}[/tex]

So that for each n in N we have:

limsup [tex]abs{\frac{z_{n+1}}{z_{n}}}[/tex] is greater than 1
 

Answers and Replies

  • #2
Dick
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How about combining the convergent series 2^(-n) and 3^(-n) in a clever way? Hint: alternate terms from each.
 
  • #3
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yeah thx, I used 2^(-n) when n is even and 2^-(n+1 ) when n is odd
 
  • #4
Dick
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yeah thx, I used 2^(-n) when n is even and 2^-(n+1 ) when n is odd
Something like that will work, but doesn't that just give you limsup=1?
 

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