Induction of inequality

I am having a hard time getting started on this.

n*3ⁿ<= 4ⁿ-2
where n>6

I have done the start step setting n = 7 and affirming that it is true.

and I assume

k*3^k<= 4^k-2

but I cannot grasp how I should prove
(k+1)*3^(k+1)<= 4^(k+1)-2

Thank you

Your inequality is very similar to the Bernoulli's inequality.

I fail to see how.

Quote:

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Originally Posted by dowant

n*3ⁿ<= 4ⁿ-2 where n>6
I have done the start step setting n = 7 and affirming that it is true.
and I assume
k*3^k<= 4^k-2

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Start from the above.

This can be proved using the auxiliary fact

for (*)

It is easily proved by induction.