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Fill in the blanks:

If P(n) : 2n < n!, n ϵ N, then P(n) is true for all n ≥ __________.

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Given; P(n): 2n < n! n ϵ N

⇒ P(1) : 2×1<1! ⇒ 2<1; it’s not true.

⇒ P(2) : 2×2<2! ⇒ 4<2; it’s not true.

⇒ P(3) : 2×3<3! ⇒ 6<6; it’s not true.

⇒ P(4) : 2×4<4! ⇒ 8<24; it’s true.

⇒ P(3) : 2×5<5! ⇒ 10<120; it’s true.

∴ n≥4

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