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I want to show that any arithmetic progression if continued long enough wouldn't contain primes. How should I proceed. Thanks- Shahab ( talk) 07:46, 22 August 2010 (UTC)
Ya don't need any [profanity removed] prime number theory to see it. Besides, it doesn't follow from th eprime number theorem since ya could get primes appearing in the sequence over and over but less frequently as n goes to INFINITY WITHOUT contradicting any bullcrap prime number theory. So no, think harder Meni Rosenfeld and Shahb. —Preceding unsigned comment added by 114.72.192.74 ( talk) 09:02, 22 August 2010 (UTC)
[irrelevant vulgarities and personal attack removed] —Preceding unsigned comment added by 110.20.58.220 ( talk) 10:25, 22 August 2010 (UTC)
[personal attacks removed] —Preceding unsigned comment added by 114.72.192.74 ( talk) 09:09, 22 August 2010 (UTC)
OK, so one of the most important lemmas on convergent series sequences is that if a series sequence converges to a limit then any subsequence also converges to that limit. This is not true for divergent series sequences, since you can take the sum of the reciprocals of the natural numbers, which diverges, and, as a subsequence, the sum of the reciprocals of the squares, which converges. My question is, if you have a sequence and you're investigating convergence, does finding a divergent subsequence imply that the sequence itself is divergent? Thanks
asyndeton
talk 11:38, 22 August 2010 (UTC)
The amended question is still confused about sequences versus series. The question about the sum of the reciprocals is about series, not sequences, whereas the lemma you mention is about sequences, not series. Michael Hardy ( talk) 19:25, 22 August 2010 (UTC)
Every sequence is a series and every series is a sequence. If an is a sequence and bn = an - an-1 and b1 = a1 then bn is a series and an can be a series. If bn is a series then its partial sums form a sequence. Every theory about sequence has one theory about series. And Meni Rosenfeld, don't dob on me mate. If I can't correct someone for the good of humanity, what can I do? And please don't say I have attacked anyone. I just asked Meni to not "dob on me mate". That's not a personal attack. I just want to better understand what I've done wrong and unless you tell me, I can't understand that. Blocking me won't help me. —Preceding unsigned comment added by 110.20.6.240 ( talk) 22:57, 22 August 2010 (UTC)
Sorry it won't happen again. I've removed "bulltwang" from my posts. Sorry again.
Mathematics desk | ||
---|---|---|
< August 21 | << Jul | August | Sep >> | August 23 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I want to show that any arithmetic progression if continued long enough wouldn't contain primes. How should I proceed. Thanks- Shahab ( talk) 07:46, 22 August 2010 (UTC)
Ya don't need any [profanity removed] prime number theory to see it. Besides, it doesn't follow from th eprime number theorem since ya could get primes appearing in the sequence over and over but less frequently as n goes to INFINITY WITHOUT contradicting any bullcrap prime number theory. So no, think harder Meni Rosenfeld and Shahb. —Preceding unsigned comment added by 114.72.192.74 ( talk) 09:02, 22 August 2010 (UTC)
[irrelevant vulgarities and personal attack removed] —Preceding unsigned comment added by 110.20.58.220 ( talk) 10:25, 22 August 2010 (UTC)
[personal attacks removed] —Preceding unsigned comment added by 114.72.192.74 ( talk) 09:09, 22 August 2010 (UTC)
OK, so one of the most important lemmas on convergent series sequences is that if a series sequence converges to a limit then any subsequence also converges to that limit. This is not true for divergent series sequences, since you can take the sum of the reciprocals of the natural numbers, which diverges, and, as a subsequence, the sum of the reciprocals of the squares, which converges. My question is, if you have a sequence and you're investigating convergence, does finding a divergent subsequence imply that the sequence itself is divergent? Thanks
asyndeton
talk 11:38, 22 August 2010 (UTC)
The amended question is still confused about sequences versus series. The question about the sum of the reciprocals is about series, not sequences, whereas the lemma you mention is about sequences, not series. Michael Hardy ( talk) 19:25, 22 August 2010 (UTC)
Every sequence is a series and every series is a sequence. If an is a sequence and bn = an - an-1 and b1 = a1 then bn is a series and an can be a series. If bn is a series then its partial sums form a sequence. Every theory about sequence has one theory about series. And Meni Rosenfeld, don't dob on me mate. If I can't correct someone for the good of humanity, what can I do? And please don't say I have attacked anyone. I just asked Meni to not "dob on me mate". That's not a personal attack. I just want to better understand what I've done wrong and unless you tell me, I can't understand that. Blocking me won't help me. —Preceding unsigned comment added by 110.20.6.240 ( talk) 22:57, 22 August 2010 (UTC)
Sorry it won't happen again. I've removed "bulltwang" from my posts. Sorry again.