Answer :

If P(r) is true then 2r ≥ 3r


For, P(r+1)


2r+1=2.2r


For, x>3, 2x>x+3


So, 2.2r>2r+3 for r>1


2r+1>2r+3 for r>1


2r+1>3r +3 for r>1


2r+1>3(r+1) for r>1


So, if P(r) is true, then P(r+1) is also true.


For, n=1, P(1):


L.H.S=2


R.H.S=3


As L.H.S<R.H.S


So, it is not true for n=1


Hence, P(n) is not true for all natural numbers.


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