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Prove the following by using the principle of mathematical induction for all :
Let P(n): I. For n = 1, P(1) : ∴ P(1) is true.II. Let the statement be true for n = m,
∴ .... (i)III. For n = m + 1, P(m + 1): or From (i),
∴ which is true.∴ P(m + 1) is true∴ P(m) is true P(m + 1) is trueHence, by the principal of mathematical induction, P(n) is true for all .