If P(n) is the statement “2ⁿ> 3n” and if P(k) is true, show that p(k+1) is also true .

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Rajesh kumar

P(n):2^n>3n We know that P(k) is true Thus ,we have 2k>_ 3k To show : P(,k+1) is true We know P(k) is true Therefore,2^k>_ 3k 2^k.2>_3k.2(multiplying both side by 2) 2^k+1>_6k 2^k+1>_3k+3k 2^k+1>_3k+3(since 3k>_3for all k) 2^k+1>_3(k+1) Hence ,P(k+1) is true