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You are not logged in. #1 20130107 08:45:52
A weird limit!Hi I know that it should be equal to 1/2 and the the Stolz theorem is supposed to be used, but I cannot get the final result... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #2 20130107 09:12:31
Re: A weird limit!Hi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20130107 09:25:07
Re: A weird limit!No. I already looked at that page. It just gets the limit to the indeterminate from 0*infinity... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #4 20130107 09:51:59
Re: A weird limit!We need to use the binomial theorem here now. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20130107 09:54:32
Re: A weird limit!Do you see the n/(p+1) part? It makes it not possible to use Stolz like that. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20130107 09:57:02
Re: A weird limit!We are not allowed to split that limit? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20130107 10:07:31
Re: A weird limit!That is right. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20130107 10:14:58
Re: A weird limit!I am trying to put it into the required form but the algebra is hideous. The above limit equals 1 / 2 . But the limit is very difficult to handle. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20130107 10:58:08
Re: A weird limit!I already got that much. That limit there is the problem... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20130107 11:04:05
Re: A weird limit!You got that far! How the heck did you get there? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20130107 11:12:44
Re: A weird limit!It wasn't hard. Last edited by anonimnystefy (20130107 11:13:11) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #12 20130107 11:42:20
Re: A weird limit!Why do you think this is a job for Stoltz then? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #13 20130107 11:51:08
Re: A weird limit!
Consider the numerator (ignoring the minus sign outside the fraction). Notice that the terms in and vanish so the highest power of is . Its coefficient is . Now look at the denominator. The highest power of is also and its coefficient is . Hence the limit as is using the following rule: If and and then Last edited by scientia (20130107 20:52:47) #14 20130107 12:17:22
Re: A weird limit!Wow! That is amazing! Thank you! Last edited by anonimnystefy (20130107 12:17:45) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #15 20130107 20:48:04
Re: A weird limit!You're welcome. 