# Let P(n) be the s

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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