EXERCITIU!

Stabiliti daca urmatorul numar este patrat perfect :

b = (1+2+3+...+2002) x 2003 x 4004

grupam:
1+2002,2+2001,3+2000
...1001+1002
avem 1001 termeni
in final obtinem 1001 x2003 x2003 x4x1001
adica 1001x2003x4,toate la patrat,
Succes!

1+2+....2002 suma lui Gauss
(1+2+...2002).2003.4004=2002.(2002+1):2.2003.4004=2002.2003.2003.4004:2=2002*2003 la patrat*2002=2002la patrat*2003la patrat —patrat perfect