Prove each of the following, for every n EN, using the Principle of Induction: + 2" 2¹*¹ — I. ... a) 1 + 2 + 4 + b) 1 x (1) + 2 × (2) + P *** + n X (n!) = (n + 1)! − 1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 21EQ
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Prove each of the following, for every nEN, using the Principle of Induction:
2¹+¹ — I.
a) 1 + 2 + 4 + ··· + 2ª
b) 1 x (1) + 2 × (2!) + ··· + n × (n!) (n + 1)! - 1.
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Transcribed Image Text:Prove each of the following, for every nEN, using the Principle of Induction: 2¹+¹ — I. a) 1 + 2 + 4 + ··· + 2ª b) 1 x (1) + 2 × (2!) + ··· + n × (n!) (n + 1)! - 1. www
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