6 real numbers, sum of any 3 consecutive is negative, while sum of any 4 consecutive is positive. Prove false.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 three consecutive a i is negative. Prove that his claim is false.

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6 real numbers, sum of any 3 consecutive is negative, while sum of any 4 consecutive is positive. Prove false.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 three consecutive       a    i   is negative. Prove that his claim is false.

Braedon Rivas · Accepted Answer

Consider the simulataneous inequalties  a  +  b  +  c  +  d  &amp;gt;  0  ,  a  +  b  +  c  &amp;lt;  0  ,  b  +  c  +  d  &amp;lt;  0.What can we say about the sign of   a? What about the sign of   d?If you have a sequence of six numbers, it has three subsequences each consisting of four consecutive numbers. Consider what each of them tells you about numbers in the original sequence.

Jackson Duncan · Accepted Answer

0  &amp;gt;  (  a  +  b  +  c  )  +  (  b  +  c  +  d  )  +  (  c  +  d  +  e  )  +  (  d  +  e  +  f  )  =  a  +  2  b  +  3  c  +  3  d  +  2  e  +  f  .  0  &amp;lt;  (  a  +  b  +  c  +  d  )  +  (  b  +  c  +  d  +  e  )  +  (  c  +  d  +  e  +  f  )  =  a  +  2  b  +  3  c  +  3  d  +  2  e  +  f  .

6 real numbers, sum of any 3 consecutive is negative, while sum of any 4 consecutive is positive. Pr

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