Principle of Ma...

A student was asked to prove a statement P ( n ) by method of induction . He proved that P ( 3 ) is true and that P(n) ⇒ P(n + 1) for all natural numbers n . On the basis of this the criteria applied on n for  P ( n ) to be  true 

3²ⁿ⁺² − 8n − 9 is divisible by 64 for all

The inequality n! > 2ⁿ⁻¹ is true

The statement 3ⁿ > 4n is true for all

The statement 2ⁿ > 3n is true for all

The statement 2ⁿ⁺² < 3ⁿ is true for all 

The smallest positive integer for which The statement 3ⁿ + 1 < 4ⁿ is true for

For all n ∈∈ N , 49ⁿ + 16n − 1is divisible by 

2³ⁿ-1 is divisible by