Question

aratati ca nr b=1+3+5+...+2011 este patrat perfect.

Answer 1

1= 1 +2·0
3 =1 +2·1
5 =1+2·2
7= 1+2·3
.........................
2011 = 1+2·1005 ⇒ b= 1·1006 +2(1+2+3+......+1005) = 1006 +2·1005·1006/2 =
= 1006 (1 +1005) =1006² =patrat perfect

Answer 2

1= 1 +2·0 3 =1 +2·1 5 =1+2·2 7= 1+2·3 ......................... 2011 = 1+2·1005 ⇒ b= 1·1006 +2(1+2+3+......+1005) = 1006 +2·1005·1006/2 = = 1006 (1 +1005) =1006² =patrat perfect