Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #3 20130803 21:24:13
Re: Easy puzzle challengeHi Nehushtan 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 #5 20130811 03:23:11
Re: Easy puzzle challengehi Nehushtan, Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20130901 17:48:24
Re: Easy puzzle challengeHi Nehushtan, Last edited by gAr (20130901 17:48:40) "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #9 20131017 23:24:14
Re: Easy puzzle challengeHi Nehushtan 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 20131017 23:59:16
Re: Easy puzzle challengeYes, but I liked this method, so I posted that. And besides, induction would require a bit of latexing, and I'm on my phone. 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 20131018 00:32:34
Re: Easy puzzle challengeHi; So obviously The summation calculus can now sum that using the rule where (r+1) and (r) are the falling factorial operator. Notice the above rule is the discrete counterpart to the integral operator. Now we finish up with 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 20131018 01:29:40
Re: Easy puzzle challengeHello: which is the binomial in the question. You should use induction to show that the formula is correct. #14 20131018 01:34:40
Re: Easy puzzle challenge
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. #15 20131018 16:37:13
Re: Easy puzzle challengeBy generating functions, start with the g.f of the triangular numbers: "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #16 20131019 00:37:23
Re: Easy puzzle challenge
That also proves the equality from #10. 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 #17 20131019 20:58:14
Re: Easy puzzle challengeThat's right. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #18 20131226 15:45:43
Re: Easy puzzle challengeJim loves to play online games. On the online games site he has just joined, he needs a fourdigit secret combination code for access. Being very bad at memorizing combinations, even fourdigit ones, he writes down his combination code and proceeds to memorize it. 134 books currently added on Goodreads #19 20131226 22:13:10
Re: Easy puzzle challenge
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. #21 20140113 22:32:48
Re: Easy puzzle challengeHi; 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. #23 20140114 00:06:02
Re: Easy puzzle challengeHi; 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. #25 20140114 00:29:30
Re: Easy puzzle challengeHi; 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. 