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  • Fill in the blanks in the following: If P(n) : 2n < n!, n ϵ N, then P(n) is true for all n ≥ __________.

Fill in the blanks in the following:

If P(n) : 2n < n!, n \in N, then P(n) is true for all n\geq __________.

Answers (1)

n\geq4

Given:

P(n) : 2n < n!, n \in N

Now, we’ll substitute different values for n,

At n = 1,

P(1) = 2 \times 1 < 1!,

            = 2 < 1, viz. not true.

At n = 2,

P(2) = 2 \times 2 < 2!

           = 4 < 2, viz. not true.

At n = 3,

P(3) = 2\times 3 < 3!

           = 6 < 6, viz. not true

At n = 4,

P(4) = 2 \times 4 < 4!

          = 8 < 24, viz. not true

At n = 5,

P(5) = 2 \times 5 < 5!

            = 10 < 120, viz. true

Therefore, n\geq4

Posted by

infoexpert21

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