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## Homework Statement

show n

^{3}+ n < 3

^{n}for all n >= 4

## Homework Equations

## The Attempt at a Solution

I.H : n

^{3}+ n <

^{n}for all n >= 4

3(n

^{3}+ n) < 3(3

^{n})

then (3

^{n+1}) = 3 x 3

^{n}

> 3((n

^{3}) + n ) by I.H

> (n+1)

^{3}+ (n+1)

if we show 3(n

^{3}+ n ) - [(n+1)

^{3}+ (n+1)] > 0 by subbin in 4 which is n >= 4, does it suffice as proof?

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