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You are not logged in. #1 20111114 07:17:42
sums of power sequencesmany more to come:D PS sorry about that last one I worked it out myself (the otehrs I got from a book years ago) I'm no good at factorising so if someone could do that for me I would be most greatful Last edited by wintersolstice (20111114 07:26:46) Why did the chicken cross the Mobius Band? To get to the other ...um...!!! #2 20111115 04:02:34
Re: sums of power sequencesHi; 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 20111117 04:58:39
Re: sums of power sequencesThanks bobbym Why did the chicken cross the Mobius Band? To get to the other ...um...!!! #4 20111117 05:03:48
Re: sums of power sequencesHi wintersolstice; 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 20111118 02:25:29#6 20120601 12:32:03
Re: sums of power sequencesI think I've got a generic format for sums of power sequences. I'm not a math expert, so maybe somebody can express this better. First, is the constraint that #7 20130308 18:24:28
Re: sums of power sequencesI know it's almost been a year since this thread's last post, but I made an "Adjusted Pascal's Triangle" to create these power sum formulas for positive integers, and I finally got around to posting it on this forum. (Putting in the n at the top of the triangle for sum of i^0 worked out perfectly, even though the formula itself cannot compute the correct value for R = 0). , and I used that to create that "Bernoulli Triangle". where , where you can calculate a Bernoulli number in terms of its predecessor Bernoulli numbers. Has anyone seen similar images like these "Adjusted Pascal Triangles" to compute the power sum and Bernoulli numbers visually? I'm curious because I never heard of either, particularly the sum of power one, in high school or college math courses. Last edited by cmowla (20130309 11:26:05) #8 20130308 23:04:21
Re: sums of power sequencesHi cmowla #9 20130330 07:41:56
Re: sums of power sequences
When I was in the process of deriving the formula which I used to create the "adjusted pascal triangle" for the sum of power formulas, I actually went through the same process that Bernoulli did for a portion of my research. which I used to create that "adjusted Pascal's Triangle" for the power sum polynomial formulas. [Step 2]: Extrapolate By applying the same pattern to different power sums, I found that a general formula for sum i^R is simply: , which has been known for a while, but I didn't know that unfortunately until after I found it. [Step 4]: Transforming into a pattern which can be generated by a diagram (which turned out to be an "adjusted Pascal Triangle") This was the trickiest part. I probably spent more time doing this step than anything else because I didn't even know if it was possible to create a formula which could generate an intuitive diagram. So we show that
Last edited by cmowla (20130330 08:15:03) 