Prove that `3^n>n^2`

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aruv | High School Teacher | (Level 2) Valedictorian

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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`




`and 3^k>2k`







`` P(k+1) is true when P(k) is true

Thus P(n) is true for al natural number.

Hence proved.