Question

1+3+5+7+.......+2005 .DEMONSTRATI CA ACEASTA SUMA ESTE PATRAT PERFECT

Answer 1

   
[tex]\displaystyle \\ 1+3+5+7+ \cdots +2005 = ? \\ \\ \text{Calculam numarul de termeni: } \\ \\ n = \frac{2005-1}{2}+1 = \frac{2004}{2}+1 = 1002+1 = \boxed{1003 ~\text{termeni}} \\ \\ \text{Calculam suma:}\\ \\ 1+3+5+7+ \cdots +2005 = \\ \\ =\frac{1003(2005+1)}{2} = \frac{1003\times 2006}{2} = 1003\times 1003 = \boxed{\bold{1003^2} = \texttt{pp}}[/tex]