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10-29-2007, 09:20 PM
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| | Problem 39 Let  . For each positive integer  let  .
Find the limit,
(Where  are possibly different integers defining a different sequence).
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10-31-2007, 02:20 AM
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| | Quote:
Originally Posted by ThePerfectHacker Let  . For each positive integer  let  .
Find the limit,
(Where  are possibly different integers defining a different sequence). | is this lim as n approaches infinity?
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10-31-2007, 07:45 AM
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| | Quote:
Originally Posted by kalagota is this lim as n approaches infinity? | When you are dealing with sequences that is the only type of limit you can have. (What else can you possibly approach  )
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10-31-2007, 10:26 AM
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| | Maybe I'm off base here, PH,:
So, we have: | 
10-31-2007, 11:09 AM
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| | Quote:
Originally Posted by galactus Maybe I'm off base here, PH,:  | The sums diverges. Because,  for sufficiently large  .
And  does not converge, it is the harmonic series.
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11-01-2007, 07:41 AM
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| | Let  .  is ascending and unbounded.
By Stolz-Cesaro, we have  .
Then | | The following users thank red_dog for this useful post: | |  | 
11-03-2007, 10:07 PM
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| | Quote:
Originally Posted by red_dog Let  .  is ascending and unbounded.
By Stolz-Cesaro, we have  .
Then  | I can do it without Stolz-Cesaro. Want to try?
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11-10-2007, 08:49 PM
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| | The key step is to note that  . That means,  .
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