# Proof of Inequality by Induction

#### sbrajagopal2690

##### New member
need help on this

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

#### Opalg

##### MHB Oldtimer
Staff member
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 $(n+1)^3 \leqslant \bigl(n+\frac n3\bigr)^3$.