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Topic: Factorial Sum (Read 8401 times) |
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ThudnBlunder
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Factorial Sum
« on: Feb 15th, 2011, 2:14pm » |
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49
Evaluate if you please  (-1)k C(99,2k) = C(99,0) - C(99,2) + C(99,4) - ......... + C(99,96) - C(99,98)
k=0
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| « Last Edit: Feb 15th, 2011, 2:17pm by ThudnBlunder » |
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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
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Re: Factorial Sum
« Reply #1 on: Feb 16th, 2011, 9:46am » |
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[ 99 C(99,k) k=0 ik + 99k=0 C(99,k) (-i)k ]/2
[(1+i)99 + (1-i)99]/2
{[ 2 epi/4 i]99 + [2 e-pi/4 i]99}/2
297 [e99 pi/4 i + e-99 pi/4 i]
297 [e3 pi/4 i + e-3 pi/4 i]
- 298
- 249
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| « Last Edit: Feb 16th, 2011, 9:48am by towr » |
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ThudnBlunder
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Re: Factorial Sum
« Reply #2 on: Feb 16th, 2011, 10:31am » |
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Nicely done, towr. 
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