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

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उत्तर

P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true.

Let P(n) be 2ⁿ < n!

So, the examples of the given statements are,

P(0) ⇒ 2⁰ < 0!

i.e 1 < 1 ⇒ not true.

P(1) ⇒ 2¹ < 1!

i.e 2 < 1 ⇒ not true.

P(2) ⇒ 2² < 2!

i.e 4 < 2 ⇒ not true.

P(3) ⇒ 2³ < 3!

i.e 8 < 6 ⇒ not true.

P(4) ⇒ 2⁴ < 4!

i.e 16 < 24 ⇒ true.

P(5) ⇒ 2⁵ < 5!

i.e 32 < 60 ⇒ true, etc.

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Principle of Mathematical Induction

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Q 1 Q 15 Q 2

पाठ 4: Principle of Mathematical Induction - Exercise [पृष्ठ ७०]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11

पाठ 4 Principle of Mathematical Induction
Exercise | Q 1 | पृष्ठ ७०

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Principle of Mathematical Induction

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