Question

For all n ∈ N, by using principle of mathematical induction, then prove that:

1 + 5 + 5² + ... + 5^{n - 1} = (5ⁿ - 1)/4

Answer 1

Let the given statement is P(n), i.e.,

Hence, P(m + 1) is also true.

Hence, by the principle of mathematical induction the given statement is true for each natural number n ∈ N.

Hence Proved.