MathDB

Write

2017

following numbers on the blackboard:

-\frac{1008}{1008}, -\frac{1007}{1008}, ..., -\frac{1}{1008}, 0,\frac{1}{1008},\frac{2}{1008}, ... ,\frac{1007}{1008},\frac{1008}{1008}

. One processes some steps as: erase two arbitrary numbers

x, y

on the blackboard and then write on it the number

x + 7xy + y

. After

2016

steps, there is only one number. The last one on the blackboard is
(A):

-\frac{1}{1008}

(B):

0

(C):

\frac{1}{1008}

(D):

-\frac{144}{1008}

(E): None of the above

Problem Statement