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You are not logged in. #1 20060305 01:45:49
*** Problems***1 Character is who you are when no one is looking. #2 20060305 04:08:45
Re: *** ProblemsThis sounded like a trick question at first, but having spent a little time on it, the pattern is somewhat surprising and gives a remarkably high number of results divisible by 3! Having worked on this the hard way, let's now try to get a formula. #3 20060305 05:35:25
Re: *** ProblemsI'm afraid not. If n = 1, then there are 9 possible combinations for the two numbers. Why did the vector cross the road? It wanted to be normal. #4 20060305 13:24:18
Re: *** ProblemsMathsy, I agree with your logic, but the question asked for two numbers to be selected at random, not the same number to be selected twice. Hence, I excluded the possibility of x=y. This has the effect of removing 3n from both numerator and denominator. Progressing through the series, up to very high values of n will still tend towards 55.55%, but always slightly less than this and, at very low values of n, significantly less. #5 20060305 13:29:11
Re: *** ProblemsAh. True point. Well, in that case, you're completely correct. If n = 1, then the probability is 1/3 and as n increases the probability will tend to 5/9 without ever reaching it. Why did the vector cross the road? It wanted to be normal. #7 20060305 16:17:11
Re: *** ProblemsGood going, mathsyperson and ashwil! I shall wait for more responses. In a day or two, I shall post the solution. Character is who you are when no one is looking. #8 20060306 00:02:08
Re: *** Problems***2 Character is who you are when no one is looking. #9 20060306 00:07:08
Re: *** Problems***3 find the sum 1² + 3²/1! + 5²/3! + 7²/5! + ............∞ Character is who you are when no one is looking. #10 20060306 00:46:54
Re: *** Problems***2 IPBLE: Increasing Performance By Lowering Expectations. #11 20060306 00:50:55
Re: *** Problems***3 IPBLE: Increasing Performance By Lowering Expectations. #12 20060306 00:55:31
Re: *** Problems***2 #13 20060306 01:06:49
Re: *** ProblemsIf you ractorize what you got as equation you'll get the above equation. IPBLE: Increasing Performance By Lowering Expectations. #14 20060306 02:42:03
Re: *** ProblemsThanks, Krassi. #15 20060306 02:51:37
Re: *** ProblemsYou mathz is (the moderators won't allow me to say this ) GOOD. IPBLE: Increasing Performance By Lowering Expectations. #16 20060306 04:56:51
Re: *** ProblemsWhat a lovely compliment! I wish that my teacher had agreed with you in 1978 (or, even the examination board!!). I was far from the perfect student and my maths was only average at best. But what I have done in life since then is to learn from mistakes, work from first principles wherever possible and always try to understand WHY things are the way they are. It may take a lot longer than remembering formulae, but it is much more sound in the longterm. #17 20060306 05:03:38
Re: *** ProblemsI used ugly algebra so I prefer you to post your proof. IPBLE: Increasing Performance By Lowering Expectations. #18 20060306 05:09:28
Re: *** ProblemsI wanted to say another thing from drags but the word blocker from the forum didn't allowed me to do it. IPBLE: Increasing Performance By Lowering Expectations. #19 20060306 15:40:59
Re: *** Problemskrassi_holmz and ashwil, I shall post the solutions (with steps) to ***2 and ***3 by the weekend! You both are on the right track, Well done! Character is who you are when no one is looking. #20 20060307 02:01:07
Re: *** Problems***4 Character is who you are when no one is looking. #21 20060307 02:15:19
Re: *** Problems
Why did the vector cross the road? It wanted to be normal. #22 20060307 02:37:50
Re: *** ProblemsExcellent, mathsyperson! Character is who you are when no one is looking. #23 20060307 15:56:28
Re: *** Problems***5 is greater than or equal to where a, b, and c are positive real numbers. Character is who you are when no one is looking. #24 20060307 23:33:28
Re: *** Problemsganesh, I am seriously struggling with the proof of ****3. I can work through the logical structure of the 4 given equations and I can see an obvious similarity with the expression to be solved. However, for the life of me, I just cannot get an expression that absolutely links this expression to those funtions of e. The problem is that the numerator's progression is a funtion of (1+2n)^2 rather than x^n, as given in the examples, which is destined to diverge greatly as n increases. #25 20060307 23:39:13
Re: *** Problemsashwil, Character is who you are when no one is looking. 