2 n n ! is true for w h e r e n ∈ N

Question

2 n n ! is true for w h e r e n ∈ N, n 4, n ≥ 4, n 3, None of these

MARKS App · Accepted Answer

P n : 2 n n ! P 1 , P 2 , P 3 are not true. P 4 : 16 24 is true P K : K ! > 2 K is true for some K ∈ N , K > 4 To prove P ( K + 1 ) : K + 1 ! > 2 K + 1 is true Multiplying both sides of P K by ( K + 1 ), we get, K + 1 ! > 2 K K + 1 > 2 K . 2 ( a s K > 4 ) Hence by PMI, P n is true ∀ n ∈ N , n ≥ 4

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