MHB Proof of Inequality by Induction

Thread starter sbrajagopal2690
Start date Jul 2, 2013
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Induction Inequality Proof

Jul 2, 2013

sbrajagopal2690

need help on this

Show by induction that n^3 <= 3^n for all natural numbers n.

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Jul 2, 2013

Opalg

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MHB

Re: Proof of Inequlity by Induction

sbrajagopal2690 said:

need help on this

Show by induction that n^3 <= 3^n for all natural numbers n.

Hint: If $n\geqslant 3$ then $(n+1)^3 \leqslant \bigl(n+\frac n3\bigr)^3$.

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