Question

$(1 + 2 + 3 + ... + 2012) \times ( \frac{1}{2012} - \frac{1}{2012 \times 2013} ) =$

Answer 1

---------------------Vezi poza----------------------

Answer 2

$\underline {Suma~Gauss}: 1+2+3+...+n=[n \cdot (n+1)]:2$
$= \{[2012 \cdot (2012 + 1)] :2 \} \cdot [ \frac{1}{2012} - ( \frac{1}{2012} - \frac{1}{2013} ] = \\ \\ =[(2012 \cdot 2013):2] \cdot (\frac{1}{2012}-\frac{1}{2012}+\frac{1}{2013})= \\ \\ \frac{2012 \cdot 2013}{2} \cdot \frac{1}{2013}= \frac{2012}{2}=1006$