[tex]\displaystyle 2+4+6+...+100= \\ \\ \texttt{Factor comun pe 2.} \\ \\ 2(1+2+3+...+50)= \\ \\ \texttt{Suma lui Gaus aplicata parantezei. } \\ \\ \boxed{\frac{n(n+1)}{2} \ ; \texttt{n=ultimul nr din sir}} \\ \\ \\ \frac{50(50+1)}{2}= \frac{\not50 \cdot 51}{\not2}= 25 \cdot 25 = 1275 \\ \\ 2\cdot1275=2550[/tex]
