Question

Aratati ca x=1004+2+4+.....+2006 este partat perfect

Answer 1

x = 1004 + 2 + 4 + .. + 2006

x = 1004 + 2·(1 + 2 + .. + 1003)

x = 1004 + 2·1003·1004 : 2

x = 1004·(1 + 1003)

x = 1004·1004

x = 1004²

Answer 2

x = 1004+2(1+2+3+...+1003) = 1004+(2x1003x1004)/2 = 1004+1003x1004 =

= 1004x(1+1003) = 1004x1004 = 1004² ⇒ patrat perfect