Prove by induction that
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Your question is not complete, for which it is required that be defined, since in the case of , the statement
is false, i.e. . So for it to be true ought to be greater than 2.
Since we must prove by induction, we will restate the question correctly. So let for , .
Basis step:
Next is the Inductive step:
We will prove that is true.
So
. We multiply both sides by 2 and obtain
Next, multiply both sides by 3 and obtain
. We now add to both side and obtain
.
Next, we add and subtract to the right hand side and obtain
Since the smallest integer permissible for the basis step is , we substitue 2 for k for the items in the parenthesis and obtain
Now the proof is complete.