Problem A2

Let a₁, a₂, ···, a_n and b₁, b₂, ···, b_n be nonnegative real numbers. Show that

(a₁a₂···a_n)^1/n + (b₁b₂···b_n)^1/n £ ((a₁ + b₁)(a₂ + b₂)···(a_n + b_n))^1/n.