That was already addressed on top. It is necessary because of induction.2. Why should we add to both sides ?
Over here we might use instead of because we want to show this holds for . In order for this statement to make any sense we need to realize that is a problem for then we have a zero denominator. There may be other reasons but this is the first one that I thought of.3. In a similar problem, having to prove
we shall prove
Why choose and then add to both sides ?