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Unformatted text preview: that your CFO’s formula agrees with yours. (b) Verify this combinatorial proof by giving an algebraic proof of this same fact. Problem 3. (a) Now give a combinatorial proof of the following, more interesting theorem: n ± ² n n 2 n − 1 = k (1) k k =1 Hint: Let S be the set of all lengthn sequences of 0’s, 1’s and a single *. (b) Now prove ( 1 ) algebraically by applying the Binomial Theorem to (1+ x ) n and taking derivatives. Creative Commons 2010, Prof. Albert R. Meyer . MIT OpenCourseWare http://ocw.mit.edu 6.042J / 18.062J Mathematics for Computer Science Spring 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.
 Spring '11
 Prof.AlbertR.Meyer
 Computer Science

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