# Prove the following using the principle of mathematical induction for all n ∈ N Let the given statement be P(n), as First, we check if it is true for n = 1, It is true for n = 1.

Now we assume that it is true for some positive integer k, such that …………..(1)

We shall prove that P(k + 1)is true,

Solving the left hand side with n = k + 1  [From equation (1)]       Which is equal to the Right hand side for n = k + 1.We proved that P(k + 1) is true.

Hence by principle of mathematical induction it is true for all n N.

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