Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: (1+ 1/1)(1+ 1/2)(1+ 1/3)...(1+ 1/N) = (N + 1)

Question

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

`(1+ 1/1)(1+ 1/2)(1+ 1/3)...(1+ 1/n) = (n + 1)`

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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Principle of Mathematical Induction

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