2n

Question

2n < n! is true for textwhere n ∈ N  (A) n < 4 (B) n≥ 4 (C) n < 3 (D) None of these

Tardigrade Admin · Accepted Answer

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

Q. $2^{n} < n!$ is true for ${where n \in N}$

$n < 4$

$n \geq 4$

$n < 3$

None of these

Q. 2n<n! is true for {wheren∈N}

n<4

n≥4

n<3

None of these

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

Q. $2^{n} < n!$ is true for ${where n \in N}$

$n < 4$

$n \geq 4$

$n < 3$