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,
Adding (k + 1) to both sides
We proved that P(k + 1) is true.
Hence by principle of mathematical induction it is true for all n ∈ N.