Hello,

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

solution:

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.

Questions:

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 ?

Thanks.