Prove by induction that for all integers n greater than or equal to 2, 2^n+1 < 3^n
This is how I would do it:
For , , , true for
Assume for , this gives you
Now the induction step, prove for
Dividing both sides by 2
Therefore if , then is definitely , true for all if true for
True for , therefore true for all integers greater than or equal to 2.
QED