1+3+5...+2017 = progresie aritmetica
[tex] a_{1}=1; a _{n}=2017, r=2 \\ \\ a _{n}=a _{1}+(n-1)*r \\ \\ 2017=1+(n-1)*2 =1+2n-2 \\ \\ 2018=2n ; n=1009 \\ \\ S=[( a_{1}+ a_{n})*n]:2= [(1+2017)*1009]:2=2018*1009:2= \\ \\ S=1009*1009=1009^{2} \\ \\ [/tex]
1+3+5...+2017=1009²
