A.trebuie clarificat enuntul
B. [tex] \frac{n ( n+1)(n+2) }{2013} [/tex]
Produsul a trei numere consecutive este divizibil cu 3,
2013 este divizibil cu 3
=> fractia se reduce cu 3
C.[tex] \frac{1+3+5....+(2n+1)]}{ 2[1+2+3+....+(n+1)} = [/tex]
[tex]= \frac{(2n+1+1)[(2n+1-1):2+1]:2 }{2(n+1)(n+1+1):2} =[/tex]
[tex]= \frac{(2n+2)(n+1):2 }{2(n+1)(n+2):2} =[/tex]
[tex]= \frac{2(n+1)(n+1):2 }{(n+1)(n+2)} = [/tex]
[tex]= \frac{(n+1)(n+1) }{(n+1)(n+2)} = [/tex]
[tex]= \frac{(n+1) }{(n+2)} [/tex]
D.[tex] \frac{n^2 +3n + 2 }{n^2 + 4n + 3} =[/tex]
[tex] =\frac{n^2 +2n+n + 2 }{n^2 + 3n +n+ 3} =[/tex]
[tex]= \frac{n(n+2)+(n + 2) }{n(n + 3) +(n+ 3)} =[/tex]
[tex] =\frac{(n+1)(n+2)}{(n+1)(n + 3)} =[/tex]
[tex] =\frac{n+2}{n+3} [/tex]
