I am trying to understand the solution to a problem
but I can't understand it. Could you explain it, please?
Here is the problem:
Prove by induction that
Instead of proving
we will prove something stronger:
Basis: , holds
Inductive step: The equation holds for n, so .
By adding to both sides we have:
, so P(n+1) holds.
1. How could someone think to prove
(ie. adding )?
2. Why should we add to both sides ?
3. In a similar problem, having to prove
we shall prove
Why choose and then add to both sides ?