Prove the following inequalities by induction. In each case, n is a positive integer. a

Chapter 22, Problem 22.5

(choose chapter or problem)

Prove the following inequalities by induction. In each case, n is a positive integer. a. 2 n 2 nC1 2 n1 1. b. .1 1 2 /.1 1 4 /.1 1 8 / .1 1 2n / 1 4 C 1 2nC1 . c. 1 C 1 2 C 1 3 C 1 4 C C 1 2n 1 C n 2 . d. 2n n < 4n . e. n n n . f. 1 C 2 C 3 C 4 C C n n 2

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