Răspuns:
Explicație pas cu pas:
[tex]1+2+3+...+n=\frac{n*(n+1)}{2} \\a=2017+2*(1+2+...+2016)=2017+2*\frac{2016*2017}{2} =1*2017+2016*2017=2017^{2}[/tex]
[tex]2n+1=(n+1)^2-n^{2}\\b=1+3+5+...+2017 = (1^2 -0^2 )+(2^2 -1^2 )+(3^2-2^2)+...+(1008^2-1007^2)=-0^{2}+1008^2=1008^2[/tex]
[tex]c=81*(1+2+3+...+49)=81*\frac{49*50}{2} =81*49*25=(9*7*5)^2[/tex]
[tex]d=2*(1+2+3+...+124)+125=2*\frac{124*125}{2}+125=124*125+1*125= 125^2=(5^3)^2=(5^2)^3=25^3[/tex]
