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You are not logged in. #1 20060111 09:25:50
Long term behaviour of sequencesDoes anyone happen to know how i could go about finding what this sequence converges to? Student: "What's a corollary?" Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary." #3 20060111 14:16:43
Re: Long term behaviour of sequencesIt sorta sounds silly, but only because you misunderstood the question. First, you have to find whether it converges or diverges. If you have a sequence An, and: Then the series diverges. Try to take this limit. Last edited by Ricky (20060111 14:17:19) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20060112 07:12:52
Re: Long term behaviour of sequencesAh yes, thanks, i've figured it. Student: "What's a corollary?" Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary." #5 20060112 07:38:49
Re: Long term behaviour of sequencesNot quite. An heads to 1/4 as n heads to infinity, that part was right. But this means the series diverges. Last edited by Ricky (20060112 07:40:02) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20060112 08:20:34
Re: Long term behaviour of sequencesI'm a bit confused by the converge/diverge thing. I thought that a sequence diverges when r>1, so it doesn't tend to any one limit? Student: "What's a corollary?" Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary." #7 20060112 08:58:04
Re: Long term behaviour of sequences(n^4 + 2n^2) / (4n^4 + 7n) #8 20060112 08:59:39
Re: Long term behaviour of sequencesThink of it this way: Where c is not 0, then basically what you are doing is: Any number that you add an infinite amount of times goes to infinity. And since An approaches this c, you are adding it an infinite amount of times. Edit: God, I'm starting to think you're right. I've gotten into a habit of hearing converge and diverge, and automatically thinking infinite series. The An is also common when doing infinite series. Wonder why (s)he didn't object to my restating of the question using summation though... Edit #2:
Starting to find that quite ironic right now. Last edited by Ricky (20060112 09:04:17) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #9 20060112 09:03:13
Re: Long term behaviour of sequencesI think i see, thanks. But i'm dealing with the sequence, not the sum of the infinite series. I wasn't too clear about the difference before, but i am now. Sorry for the misunderstaning Last edited by yonski (20060112 09:05:10) Student: "What's a corollary?" Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary." 