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Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: 1.3 + 3.5 + 5.7 + ...+(2n -1)(2n + 1) = (N(4n^2 + 6n -1))/3 - Mathematics

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प्रश्न

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

1.3 + 3.5 + 5.7 + ...+(2n -1)(2n + 1) = `(n(4n^2 + 6n -1))/3`
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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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अध्याय 4: Principle of Mathematical Induction - Exercise 4.1 [पृष्ठ ९४]

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एनसीईआरटी Mathematics [English] Class 11
अध्याय 4 Principle of Mathematical Induction
Exercise 4.1 | Q 7 | पृष्ठ ९४

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