1.
Show P(1) is true
Assume P(k) is true and let where k is a fixed arbitrary integer.
Show P(k+1) is true
Hint: multiple P(k) by 3 and and remember positive terms can be dropped from the inequality.
P(k)
P(k+1)
Try to show that P(k+1) will definately be true "if" P(k) is true.
Therefore, write P(k+1) in terms of P(k) in order to draw a comparison.
Proof
"If" P(k) is true, then
Hence, if P(k) is true, then P(k+1) is true, since
Now all you need do is prove P(k) is true for the first relevant value of "n".