- #1
loli12
Hi, I was asked to determine which values of n, 3^n > n^3.
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
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