Thread: Proof of mathematical induction inequality

Hi,

Im having trouble trying to prove the following:

n^2 > 2n; n ≥ 3

Make first an equation out of it and try to understand how these numbers relate

In order to prove it by induction u have to prove that it is true for n=3
and then assume that it is true for some n and that it then follows for n+1
So
Step one:
Is it true for 3?
3^2>2*3......True!
Good not we assume that it is true for n and prove that it then follows for n+1.


(n+1)^2>2*(n+1)
n^2+2n+1>2n+1
and almost done now =).
n^2>2n by our first assumtion.
so we can subtract that from the inequality.
then we are left with 2n+1>1
and since n=positive number clearly this is true...
Hope I was clear enough can you take it from here
?
Regards Henry

hi
let
Clearly since ,now assume to prove we must prove ...
i'll let you do that .

Thanks for the replies.

when I tried to do it I got as far as:


I wasn't aware I could subtract from the inequality.

Originally Posted by blackhug

Thanks for the replies.

when I tried to do it I got as far as:


I wasn't aware I could subtract from the inequality.

In that case you can simply write

?

2k+1 is common to both sides so it is redundant,
hence we can eliminate it.

?

This is true for k>1