Question

Care este diferenta dintre suma primelor 1000 de numere naturale pare nenule si suma primelor 1000 de numere naturale impare ?

Answer 1

(2+4+6+8+.....2000)-(1+3+5+........1999)=
2(1+2+3+.....1000)-(1+1+2+2+3+3+4+.......999+1000)=
2x(1000x1001):2-[2(1+2+3+...999)+1000]=
1001000-[2(999X1000):2+1000]=
1001000-(999000+1000)=
1001000-1000000=1000