Basic Mathematics & Logarithm
Mathematical Induction
nta_abhyas_2025
Grade 11

Question:

$2^n < n!$ is true (where $n \in \mathbb{N}$)

Step-by-Step Solution

Key Concept: Use mathematical induction to verify that the inequality holds for all natural numbers beyond a certain threshold
$P(n): 2^n < n!$. $P(1), P(2), P(3)$ are not true. $P(4): 16 < 24$ is true. $P(k): k! > 2^k$ is true for some $K \in \mathbb{N}, K > 4$.
Correct Answer: 2

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