Answer :

To Prove:



Let us prove this question by principle of mathematical induction (PMI)


Let P(n):


For n = 1


LHS =


RHS = = 2


Hence, LHS = RHS


P(n) is true for n = 1


Assume P(k) is true


= …(1)


We will prove that P(k + 1) is true


RHS =


LHS =


[Now writing the second last term ]


=


= [ Using 1 ]


=


=


= k + 2


= RHS


LHS = RHS


Therefore, P (k + 1) is true whenever P(k) is true.


By the principle of mathematical induction, P(n) is true for


where n is a natural number


Hence proved.


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