Given and for n ≥ 2, where a > 0, A > 0.

Prove that




Step1: For n=1




As LHS=RHS.


So, it is true for P(1)


For n=k, let P(k) be true.



Now, we need to show P(k+1) is true whenever P(k) is true.


P(k+1):









As L.H.S=R.H.S


Thus, P(k+1) is true. So, by the principle of mathematical induction


P(n) is true for all n.


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