# Proof by induction?

• Mar 12th 2007, 03:37 PM
chixor1
Proof by induction?
Im struggling on a problem ive been given in class and was wondering if anyone could point me in the right direction for the solution?

The question is:

Prove that n^2>=2n+3 for n>=3

Am i correct in assuming this is proof by induction?
So would I then do n=k
so k^2>=2k+3

Then do I do n=k+1??
• Mar 12th 2007, 05:14 PM
ThePerfectHacker
Quote:

Originally Posted by chixor1
Im struggling on a problem ive been given in class and was wondering if anyone could point me in the right direction for the solution?

The question is:

Prove that n^2>=2n+3 for n>=3

Is it true for n=3. Indeed.

k^2>=2k+3

k^2+2k>=2k+2k+3

k^2+2k+1>=2k+2k+3+1=(2k+2)+(2k+2)>=(2k+2)+3=2(k+1) +3
• Mar 13th 2007, 06:25 PM
slobone
Proof by induction always has two parts.

Base step. Show that the statement is true for some minimal integer n. In this case, you want n = 3 because you're not interested in any integer lower than that.

So in the base step you need to show that 3^2 >= 2(3) + 3.

(Base step is usually the easy part.)

Inductive step. Here you need to show that if the statement is true for n, then it's also true for n + 1.

So you can make the assumption that for some arbitrary given integer n, it has already been shown that n^2 >= 2n + 3.

You can use this to show that it must follow that (n + 1)^2 >= 2(n + 1) + 3. I would start by simplifying the equation, then compare what you get with what you already know.