Question

Efectuati:
a) (343-1^3) x (343-2^3) x ...x(343-2003^3)=
b)[(1+2+3+...+2010) x (2011-1-2-3-...-2010)^2]:(2011^2 x 1005)=
1^3=1 la puterea a treia

Answer 1

Folosim formula lui Gauss: b).[(1+2+3+....+2010)×(2011-1-2-3-......-2010)^2]÷(2011^2×1005)={(2010×2011)/2×[2011-(1+2+3+....+2010)]^2}÷(2011^2×1005)=[(1005×2011)×(2011-1005×2011)]÷ (2011^2×1005)=[(1005×2011)×2011(1-1005)]÷(2011^2×1005)=-1004×(2011^2×1005)÷(2011^2×1005)=-1004