Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: (1+3/1)(1+ 5/4)(1+7/9)...(1 + ((2n + 1))/N^2) = (N + 1)^2 - Mathematics

प्रश्न

Prove the following by using the principle of mathematical induction for all n ∈ N:

(1+3/1)(1+ 5/4)(1+7/9)...`(1 + ((2n + 1))/n^2) = (n + 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 13 Q 12 Q 14

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 13 | पृष्ठ ९५

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Principle of Mathematical Induction

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