NTA Abhyas JEE Main2020MathematicsMathematical InductionPractice
2 n < n ! is true for w h e r e n ∈ N
Options
- An < 4
- Bn ≥ 4
- Cn < 3
- DNone of these
Correct answer
B. n ≥ 4
Step-by-step solution
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