consider the expansion

(1-a)(1-b)(1-c)(1-d)...=1-a-b+ab-c+ac+bc-abc-d+...

what is the sign of the n-th term ?

送交者: 短江学者 于 2007-09-30, 19:50:29:

回答: consider the expansion 由 找老婆专用ID 于 2007-09-30, 11:47:34:

Let the first expansion term be called the 0th term and the second term the 1st term etc. Convert n into binary, add all the bits according to Boolean algebra, then the sum zero indicates a positive sign for the nth term. Otherwise negative. For example, n=7, binary 111, sum to 1 , this says that the 7th term has a negative sign.