Question

[ clasa a V-a ] Aratati ca numarul a=1+2+3+...+264+265·133 este patrat perfect

Answer 1

a=1+2+3+4+....+264+265 x 133
a=(1+264) + (2+263)+...+(132+133) +265 x 133
a= 265 x 132(sunt 132 de perechi cu suma 265) + 265 x 133
a= 265(132+133)
a= 265 x 265
a= 265², deci e pătrat perfect.

Answer 2

a=1+2+3+4+..........+264+265x133=
264x(264+1):2+35245=
264x265:2+3+35245=
69960:2+35245=
34980+35245=70225
70225=265x265