My way for doing induction problems.

 Proof questions are nightmares for most student.

There are two way--mathematical induction and complete induction for solving different problem.
However, I find using mathematical induction more often than using complete induction.
What 3 steps I used for proving statements:
First step: Define P(n).
  In order to do so, I will read question really carefully to get what kind of  P(n) I have to define and what n means in P(n).

Examples:
the square of b is greater than double of itself when b is a natural number greater than 2.
then P(n) would be: sqr(n)>2n.

Second step:Finding base cases for P(n).
  For this step, always find the eaziest case but the smallest case that P(n) is true. That u will be able to find the range of n.

Examples:

For sqr(n)>2n.
Find P(n) is true for n=3.

Third step:(most important steps)Induction steps
For mathematical induction using P(n)=>P(n+1) to prove all n is true for P(n)

Examples:
  if P(n) is true. then prove P(n+1)
       for the examples about just to find the different between sqr(n+1) and sqr(n) is greater than or equal to 2(n+1)-2(n).


Complete Induction has first two similar steps but the third steps will be (P(0),P(1),...P(n)=>P(n+1)) =>P(n).

That is how I did for proof questions using induction method.