Question 18:
Prove the following by using the principle of mathematical induction for all n ∈ N:
Answer
Let the given statement be P(n), i.e.,
We shall now prove that P(k + 1) is true whenever P(k) is true.
Consider
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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