Q8 of 66 Page 12

Prove the following by the principle of mathematical induction:

Let P(n):


Step1: Let us verify P(1).


P(1):


P(1):


Therefore, P(1) is true.


Step 2:


Let P(k) is true.


Therefore, P(k):


Now we have to prove that P(k + 1) is also true.


So,


L.H.S =


L.H.S =


Now from P(k) we can say that,



Putting this value, we get,


L.H.S =


L.H.S =


L.H.S =


L.H.S = R.H.S


Hence, Proved.


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