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Topic: Combinatorial Sum (Read 1592 times) |
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ThudnBlunder
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The dewdrop slides into the shining Sea
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Combinatorial Sum
« on: Jan 20th, 2009, 5:09am » |
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49 Evaluate (-1)k 992k = 990 - 992 + 994 - ....... - 9998 k=0
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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towr
wu::riddles Moderator Uberpuzzler
Some people are average, some are just mean.
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Re: Combinatorial Sum
« Reply #1 on: Jan 20th, 2009, 7:50am » |
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1/2 sumn=0..99 C(99, n) in 1(99-n) + 1/2 sumn=0..99 C(99, n) (-i)n 1(99-n) ((1+i)99+(1-i)99)/2 [sqrt(2)99 exp(99 * 2pi * 1/8 i) + sqrt(2)99 exp(99 * 2pi * 7/8 i)]/2 248.5 [exp(6*pi/8 i) + exp(10*pi/8 i)] 248.5 * -sqrt(2) -249
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« Last Edit: Jan 20th, 2009, 7:52am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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pex
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Re: Combinatorial Sum
« Reply #2 on: Jan 20th, 2009, 8:45am » |
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So, more generally, sumk=0..floor(n/2) (-1)k nC2k =hidden: | 2n/2 ......... if n = 0 mod 8 2(n-1)/2 ... if n = +- 1 mod 8 0 ............. if n = +- 2 mod 8 - 2(n-1)/2 ... if n = +- 3 mod 8 - 2n/2 ........ if n = 4 mod 8. | Interesting!
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