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  • Give an example of a statement P(n) which it true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer.

Give an example of a statement P(n)  which it true for all n \geq 4 but P(1), P(2) \: \: and \: \: P(3) are not true. Justify your answer.

Answers (1)

Given:
P(n)  which it true for all n \geq 4 but P(1), P(2) \: \: and \: \: P(3) are not true.

Let us consider P (n) be 2^n< n!

Examples of the given statements are-

P (0) \rightarrow 2^0<0! i.e., 1<1 \rightarrow Not True

P (1) \rightarrow 2^1<1! i.e., 2<1 \rightarrow Not True

\\P (2) \rightarrow 2^2<2!\: \: i.e., 4<2 \rightarrow Not True\\ P (3) \rightarrow2^3 < 3!\: \: i.e., 8<6 \rightarrow Not True\\ P (4) \rightarrow 2^4< 4!\: \: i.e., 16<24 \rightarrow True\\ \&P (5) \rightarrow 2^5<5! \: \: i.e., 32<60 \rightarrow True...... \& so on.
 

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