Hello, I had this on my exam today, I was positive that I'd be able to deal with inequalities but for some reason this one threw me off. I had to prove
for all positive integers i.e n=0,1,2,3..
anyone mind throwing some hints?
It's straight forward.
I will show you the inductive step.
Proof:
We assume , and wish to prove .
By implication it is expressed as
So if we can start from and end our proof with , we are home free.
Let's begin with . Multiplying through with , we obtain
. Observe
So we succeeded.