Question

Determinati numarul natural n pentru care:
1+3+5+...+(2n+1)+(2n-1)=625

Answer 1

1+3+5+....+2n+1=1+2+3+4....+2n+2n+1-(2+4+....+2n)=(2n+1)(2n+2)/2-2(1+2+3+...+n)=(2n+1)(2n+2)/2-2xn(n+1)/2=(4n^2+6n+2-2n^2-2n)2=(2n^2+4n+2)2=625, sau 2n^2+4n-1248=0....delta =100, rezulta n=24 si n=-26