Prove that `3^n>n^2`
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Let P(n) : `3^n>n^2` be statement ,
To prove P(n) is true for all natural number . We prove it by princple of mathematical induction.
P(1) : `3^1 >1^2=1` which is true.
Let P(k) is true .
P(k) : `3^k > k^2` is true.
To prove P(k+1) is true when P(k) is true.
P(k+1) : `3^(k+1) > (k+1)^2`
`` P(k+1) is true when P(k) is true
Thus P(n) is true for al natural number.
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