h4 - A Prove by induction that cardinality oF P A is 2 n...

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[50] Homework 4. Proof Techniques Each problem is worth 10 points [10] Show that 5 5 is irrational. [10] The harmonic number H n is defined as for n 1 H n = n summationdisplay k =1 1 k . Prove by induction that H 2 n 1 + n 2 whenever n is a nonnegative natural number. [10] Let A be a set of cardinality n . Let P ( A ) be the power set, that is, the set of all subsets
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Unformatted text preview: A . Prove by induction that cardinality oF P ( A ) is 2 n , that is, | P ( A ) | = 2 n . [10] Prove using induction that For any natural n n s i =1 1 i 2 ≤ 2-1 n [10] Derive an explicit Formula For the Following recurrence For n ≥ 1 a n = n 2 a n-1 with a = 1. 1...
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