(a) For n = 3 let X3 = {1, 2, 3}. Now consider the sum where pA...
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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.
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Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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