Answer :

To Prove:



Steps to prove by mathematical induction:


Let P(n) be a statement involving the natural number n such that


(i) P(1) is true


(ii) P(k + 1) is true, whenever P(k) is true


Then P(n) is true for all n ϵ N


Therefore,


Let P(n):


Step 1:


P(1) =


Therefore, P(1) is true


Step 2:


Let P(k) is true Then,


P(k):


Now,



=


=


=


=


= P(k + 1)


Hence, P(k + 1) is true whenever P(k) is true


Hence, by the principle of mathematical induction, we have


for all n ϵ N


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