Let the scores a(i) be generated by a (i) = [i/(n+ 1)], for i = 1,

Let the scores a(i) be generated by a_ϕ(i) = ϕ[i/(n+ 1)], for i = 1, . . . , n, where ∫¹₀ ϕ(u) du = 0 and ∫¹₀ ϕ²(u) du = 1. Using Riemann sums, with subintervals of equal length, of the integrals ∫¹₀ ϕ(u) du and ∫¹₀ ϕ²(u) du, show that Σⁿ_i=1 a(i) ≈ 0 andΣⁿ_i=1 a²(i) ≈ n.