- #1

I think this inequality holds for all intergers. But I have trouble proving it..

I checked n=1 which the inequality holds, then assume true for n.

for n+1 case:

3^(n+1) > (n+1)^3

3*3^n > (n+1)^3

i know that 3*3^n > 3n^3. But is there a way to show that 3n^3 > (n+1)^3?

and also, even i proved that to be right, it's only valid for n>= 4, how should i show that for n< 4 ?

Please give me some idea for that! Thanks