If P(r) is true then 2r ≥ 3r
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):
So, it is not true for n=1
Hence, P(n) is not true for all natural numbers.
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