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Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: `1+2+ 3+...+N<1/8(2n +1)Sqrt2 - CBSE (Arts) Class 11 - Mathematics

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Question

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

Solution

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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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 4: Principle of Mathematical Induction
Q: 18 | Page no. 95

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