Question
Mathematical Induction
Prove that 2n < n! for all n >= 4. (Note that here your base case for induction is when n = 4. You can easily check that this stement is false for n = 1,2, and 3.)
Explanation / Answer
2 power n = 4 is proved from the java program below. It is listed for first 15 Integers. package Math; public class MathCS { public static void main(String[] args) { try { int factorial; for (int i = 1; i 2 3! = 6 2 Power 3 > 6 4! = 24 2 Power 4 < 24 5! = 120 2 Power 5 < 120 6! = 720 2 Power 6 < 720 7! = 5040 2 Power 7 < 5040 8! = 40320 2 Power 8 < 40320 9! = 362880 2 Power 9 < 362880 10! = 3628800 2 Power 10 < 3628800 11! = 39916800 2 Power 11 < 39916800 12! = 479001600 2 Power 12 < 479001600 13! = 1932053504 2 Power 13 < 1932053504 14! = 1278945280 2 Power 14 < 1278945280 15! = 2004310016 2 Power 15 < 2004310016 Please rate this answer.