Question

give an example of a statement P(n) such that it is true for all n € N
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Answer 1

Answer:

Hence, by the Principle of Mathematical Induction P(n) is true for all natural numbers n. Example 5 2n + 1 < 2n, for all natual numbers n ≥ 3. 2(k + 1) + 1 =2 k + 3 = 2k + 1 + 2 < 2k + 2 < 2k . ... Hence, by the Principle of Mathematical Induction P(n) is true for all natural numbers, n ≥ 3.