Use mathematical induction to prove that n! ≥ 2n−1 whenever n is a positive integer.

Name: Use mathematical induction to prove that n! ≥ 2n−1 whenever n is a positive integer.
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Question

Quizplus · Accepted Answer

The Answer is The basis step follows since

1 ! = 1 = 2 ^ { 0 }

. For the inductive hypothesis assume that

n ! \geq 2 ^ { n - 1 }

. Then

( n + 1 ) ! = ( n + 1 ) \cdot n ! \geq ( n + 1 ) \cdot 2 ^ { n - 1 } \geq 2 \cdot 2 ^ { n - 1 } = 2 ^ { n }

.

Use Mathematical Induction to Prove That N! ≥ 2n−1 Whenever