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#### sbrajagopal2690

##### New member

- Jul 2, 2013

- 2

need help on this

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

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

- Thread starter sbrajagopal2690
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- Thread starter
- #1

- Jul 2, 2013

- 2

need help on this

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

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

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- #2

- Feb 7, 2012

- 2,703

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

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