``` wu :: forums (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi) 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                                                                                                                                                                                49Evaluate 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}/2http://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.  :) Powered by YaBB 1 Gold - SP 1.4! Forum software copyright © 2000-2004 Yet another Bulletin Board