Question

F : R->R. F(x)=x-3
S=F(1)+F(2)+F(3)+......F(2013)
Si mi se mai da ca suma divide 12

Answer 1

F(1) = 1-3 = -2
F(2) = 2-3 = -1
F(3)  = 3-3 = 0
F(4) = 1
F(5) = 2
F(6) = 3
......
F(2013) = 2013-3 = 2010

S = (-2) + (-1) + 0 + 1 + 2 + 3 + ....+2010 = -3 + (1+2+3+...+2010) = -3 + (2011*2010/2) = -3 + 2021055 = 2021052

2021052 : 12 = 168421, deci S este divizibil prin 12