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Proof of Inequality by Induction

sbrajagopal2690

New member
Jul 2, 2013
2
need help on this

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

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,703
Re: Proof of Inequlity by Induction

need help on this

Show by induction that n^3 <= 3^n for all natural numbers n.
Hint: If $n\geqslant 3$ then $(n+1)^3 \leqslant \bigl(n+\frac n3\bigr)^3$.