Question

sa se arate ca numarul 2+4+6+...+2012+2014+1008 este patrat perfect

Answer 1

2+4+6+...+2014.+.1008 =
2(1+2+3+...+1007) + 1008 =
2(1007*1008/2) + 1008 =
    1007*1008 + 1008 =   
        1008(1007+1) =
               = 1008²

Answer 2

2+4+6+..+2014+1008 =
=2(1+2+3+...+1007)+1008 
=2·1007·1008:2+1008
=1007·1008+1008
=1008(1007+1)
= 1008²