Principle of Ma...

The inequality 2ⁿ + 1 < n! is true for :

For each n ∈ N,a²ⁿ⁻¹ + b^{2n − 1} is divisible by :

For each n ∈ N , n (n + 1 ) ( 2n + 1 ) is divisible by :

For each n ∈ N , 3(5²ⁿ⁺¹) + 23ⁿ⁺¹ is divisible by :

For each n ∈ N , 2³ⁿ⁻¹ is divisible by :

For each n ∈ N , 3²ⁿ⁻¹ is divisible by :

The statement P ( n ) : “(n + 3)² > 2ⁿ⁺³ “ is true for :

The smallest positive integer ‘ n ‘ for which 2ⁿ(1×2×3×...............×n) < nⁿ holds is :

If 10ⁿ + 3 × 4ⁿ⁺¹ + k is divisible by 9 for all n ∈ N , then the least positive integral value of k is :