(a) Develop a recursive definition for the addition of n real numbers x1, x2, .. ., xn, where n > 2.
(b) For all real numbers x1, x2, and x3, the associative law of addition states that x1 + (x2 + x3) = (x1 + x2) + x3. Prove that if n, r ∈ Z+, where n > 3 and 1 < r < n, then
(x1 + x2 + ∙ ∙ ∙ + xr) + (xr+1 + ∙ ∙ ∙ + xn) = x1 + x2 + + ∙ ∙ ∙ + xr + xr+l + ∙ ∙ ∙ + xn.