(a) Develop a recursive definition for the multiplication of n real numbers x1, x2, . . . , xn, where n > 2.
(b) For all real numbers x1, x2, and x3, the associative law of multiplication states that x1 (x2x2) = (x1x2)x3. Prove that if n, r ∈ Z+, where n > 3 and 1 < r < n, then
(x1x2 ∙ ∙ ∙ xr)(xr+1 ∙ ∙ ∙ xn) = x1x2 ∙ ∙ ∙ xrxr+1 ∙ ∙ ∙ xn,