# Math Help - Binomial Theorem

1. ## Binomial Theorem

A computer programmer claims that he generated six real numbers a_1, a_2,...,a_6 so that the sum of any four consecutive a_i is positive,
but the sum of any 3 consecutive a; is negative. Prove that his claim
is false.

thanx 4 the help

2. $a_1+a_2+a_3+a_4>0$ and $a_1+a_2+a_3<0$ therefore $a_4>0$. Following this idea you get $a_5>0$ and $a_6>0$. But then how can $a_4+a_5+a_6$ be negative?!