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riddles >> putnam exam (pure math) >> Factorial Sum
(Message started by: ThudnBlunder on Feb 15th, 2011, 2:14pm)

Title: Factorial Sum
Post by ThudnBlunder on Feb 15th, 2011, 2:14pm
                                                                                                                                                                               49
Evaluate if you please http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif(-1)k C(99,2k) = C(99,0) - C(99,2) + C(99,4) - ......... + C(99,96) - C(99,98)
                                                                                                                                                                         k=0

Title: Re: Factorial Sum
Post by towr on Feb 16th, 2011, 9:46am
[hide]
[ http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif99 C(99,k) k=0 ik + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif99k=0 C(99,k) (-i)k ]/2
[(1+i)99 + (1-i)99]/2
{[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 epi/4 i]99 + [http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 e-pi/4 i]99}/2
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif297 [e99 pi/4 i + e-99 pi/4 i]
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif297 [e3 pi/4 i + e-3 pi/4 i]
- http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif298
- 249
[/hide]

Title: Re: Factorial Sum
Post by ThudnBlunder on Feb 16th, 2011, 10:31am
Nicely done, towr.  :)



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