For every positive integral value of n,{3^n} | vedclass

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(C) To determine the values of $n$ for which ${3^n} > {n^3}$,we test small positive integers:For $n = 1$: ${3^1} = 3$ and ${1^3} = 1$. Since $3 > 1$,t

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$n \geq 4$

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(C) To determine the values of $n$ for which ${3^n} > {n^3}$,we test small positive integers:For $n = 1$: ${3^1} = 3$ and ${1^3} = 1$. Since $3 > 1$,the condition holds.For $n = 2$: ${3^2} = 9$ and ${2^3} = 8$. Since $9 > 8$,the condition holds.For $n = 3$: ${3^3} = 27$ and ${3^3} = 27$. Here $27 = 27$,so the condition ${3^n} > {n^3}$ does not hold.For $n = 4$: ${3^4} = 81$ and ${4^3} = 64$. Since $81 > 64$,the condition holds.For $n = 5$: ${3^5} = 243$ and ${5^3} = 125$. Since $243 > 125$,the condition holds.By mathematical induction,it can be shown that for all $n \geq 4$,the inequality ${3^n} > {n^3}$ is true.

For every positive integral value of $n$,${3^n} > {n^3}$ when

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