(a) For n = 3 let X3 = {1, 2, 3}. Now consider the sum

where pA denotes the product of all elements in a nonempty subset A of X3. Note that the sum is taken over all the nonempty subsets of X3. Evaluate this sum.
(b) Repeat the calculation in part (a) for s2 (where n = 2 and X2 = {1, 2}) and s4 (where n = 4 and X4 = {1, 2, 3, 4}).
(c) Conjecture the general result suggested by the calculations from parts (a) and (b). Prove your conjecture using the Principle of Mathematical Induction.

Transcribed Image Text:

53 = ī + 2 + 3 + 1.2 + 1.3 + 2.3 + 1-2-3 Σι.