Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: `1+2+ 3+...+N<1/8(2n +1)Sqrt2 - Mathematics

प्रश्न

Prove the following by using the principle of mathematical induction for all n ∈ N: `1+2+ 3+...+n<1/8(2n +1)^2`

उत्तर

Let the given statement be P(n), i.e.,

Thus, P(k + 1) is true whenever P(k) is true.

Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.

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Principle of Mathematical Induction

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Q 18 Q 17 Q 19

पाठ 4: Principle of Mathematical Induction - Exercise 4.1 [पृष्ठ ९५]

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एनसीईआरटी Mathematics [English] Class 11

पाठ 4 Principle of Mathematical Induction
Exercise 4.1 | Q 18 | पृष्ठ ९५

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Principle of Mathematical Induction

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