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You are not logged in. #1 20130331 11:31:44
Convergence of (n!)^2/(kn)!The problem is: My Answer: For series to be convergent the next inequality should be true (by the Ratio Test): Since we know that both k and n are positive we can omit absolute bars. And now I simplify: But since k is a constant this limit will never be less than 1. Therefore the series divergent for all possible k. Did I make a mistake somewhere? Textbook is looking for a convergent series... #2 20130331 12:10:38
Re: Convergence of (n!)^2/(kn)!Hi; Something is wrong right 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. #4 20130331 13:02:41
Re: Convergence of (n!)^2/(kn)!Your first line is good. Shouldn't manipulations maintain equality with the original assertion? That does not? 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 20130331 13:09:23
Re: Convergence of (n!)^2/(kn)!
The second line is not correc(k(n+1))!=1*2*3*...*(k(n+1)1)*(k(n+1)) 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 20130331 13:14:01
Re: Convergence of (n!)^2/(kn)!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. #7 20130331 13:17:31
Re: Convergence of (n!)^2/(kn)!Well, the rest of his current work is okay. But that error is messing up the whole thing. 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 #9 20130401 10:32:10
Re: Convergence of (n!)^2/(kn)!Third line  in the denominator you have k1*k2*...*kn and you say below it "n times". It should be 1*2*...*kn and below it should be "kn times". 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 #11 20130401 14:44:27
Re: Convergence of (n!)^2/(kn)!Everything else seems okay to me. 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 