Odd number squared.

[crazed]

RIGHT. So, we've been set the task to prove why an odd number squared gives you an odd number. This has to be done with the use of a formula (he said something about linear and geometric formula) but I just can't get my head around it :S I googled it and everything! + Rep to anyone who can lend a hand :)

[dbgtz]

an odd number + an odd number = even therefore +another odd makes it odd again
so like:
3+3=6 +3=9
5+5= 10 +5+5= 20+5 =25
i think thats why so a formula around that

ill take a quick think

[dbgtz]

n^2=2(n+p)+x

p = previous n
n 1-3-5--7--9
x 1 9 25 49 81

if you were to word it right i think thats correct.

[crazed]

n^2=2(n+p)+x

p = previous n
n 1-3-5--7--9
x 1 9 25 49 81

if you were to word it right i think thats correct.

Ah I see, but what is X?

[kk.]

you could do proof by exhaustion i spose.

so you'd do:

1x1 = 1
3x3 = 9
5x5 = 25
7x7 = 49
9x9 = 81

and then say when it goes above 10, its

11x11 = 10x1 + 10x1 + 10x10 + 1x1

as an odd x even = even, and evenxeven = even, you only need the last to be odd. i doubt this would be the method theyre after, though

---------- Post added 14-07-2010 at 11:11 PM ----------

oh, i just googled it.

basically, an odd number can be defined as: 2k+1, where k is any constant (any integer).

n^2, where n is the odd integer

n = 2k+1

= (2k+1)(2k+1)
= 4k^2 + 4k + 1
= 2(2k^2 + 2k) +1

since 2k^2 + 2K is even, n^2 for n is an odd integer must be odd (due to the +1)

[N!ck]

Essentially what kk just said.

We can define an even number as 2n (where n is any integer) as 2 * any integer is even by definition. Therefore we can define (2n +1) as an odd number (since an even number + 1 is always odd).

So, we square the odd number, (2n + 1)

(2n + 1)^2 = (2n +1)(2n +1)

= 4n^2 + 4n +1

= 2(2n^2 +2n) + 1

Now, the bracket (2n^2 +2n) is always going to be an integer since n is an integer. As discussed above, 2 * an integer is even by definition. Therefore 2(2n^2 +2n) must be even. When we add 1 to this we always get an odd number. Therefore an odd number squared must always be odd.

[dbgtz]

Ah I see, but what is X?

sorry i didnt word that right
in the equation that x = the last number squared
like i said i cant word these things right :P


Also I'm pretty sure that equation isn't on this because if n=1 for it then it is
=2(2^2 +2) + 1
=8+4+1
=13
which doesn't make much sense

[kk.]

sorry i didnt word that right
in the equation that x = the last number squared
like i said i cant word these things right :P


Also I'm pretty sure that equation isn't on this because if n=1 for it then it is
=2(2^2 +2) + 1
=8+4+1
=13
which doesn't make much sense

All I'm going to say is you're forgetting the rules of BODMAS or BIDMAS, whichever you were taught

[dbgtz]

Ive never been taught either of then, my teacher says do it in order w/e the hell that means
so following it (i googled it) i got the same result as i did there?

[kk.]

B - brackets
O/I - indices or powers of
D - division
M - multiplication
A - addition
S - subtraction

I can't believe you've never been taught this :S it's fundamental for gcse maths o_O

=2(2 x 1^2 + 2x1) + 1
=2(2x1 + 2) + 1
=2(4) + 1
=9

Since the odd number is defined by n=2k + 1, where k is any integer, n=3, n^2=9 which is correct

[N!ck]

Ive never been taught either of then, my teacher says do it in order w/e the hell that means
so following it (i googled it) i got the same result as i did there?

Yeah, you did it correctly.

Edit: my bad I was looking at your working out, not the original equation.

[kk.]

Yeah, you did it correctly.

Unless this was sarcasm, he didn't.
2n^2 does not mean (2n)^2, which was where he went wrong

[N!ck]

Unless this was sarcasm, he didn't.
2n^2 does not mean (2n)^2, which was where he went wrong

I already corrected myself.

I was looking at (2(2^2 +2) + 1) rather than the original.

[kk.]

dw, I came in before you corrected so didn't see it :P

[dbgtz]

no i was saying n=1 so 2x1=2 still
i also searched bidmas and used a premade thing.

[kk.]

no i was saying n=1 so 2x1=2 still
i also searched bidmas and used a premade thing.

Yes, but you had 2x2=4. Trust me, go through it yourself, or look at my working, and make sure you square just the 1.

---------- Post added 15-07-2010 at 11:13 AM ----------


no i was saying n=1 so 2x1=2 still
i also searched bidmas and used a premade thing.

Also, it doesn't help that you're going from nicks, and I'm using mine, since I have n = 2k+1, so in mine, k=1

[dbgtz]

what you mean im going from nicks? :S

[kk.]

Nicks equation that he wrote. He has 2n+1, I have 2k+1.
If you're not willing to go through and accept it there's no point in carrying on. I know im right, and if you don't want to accept that, enjoy failing maths, be it at gcse or a level because you will need to know bidmas

In fact, try it on your calculator, it has it programmed to do it.

[N!ck]

what you mean im going from nicks? :S

What he said also applies to mine.

Ok, I said an odd number can be defined as (2n + 1). The odd number you selected is 1.

(2n + 1) = 1 therefore n = 0 in this case.

If you follow 2(2n^2 +2n) + 1 through with n = 0 you will get 1.

So, if your chosen odd number is 3,

(2n + 1) = 3 so n = 1

Follow it through with n = 1 and you get 9.

[dbgtz]

i said n=1 in mine not the whole equation = 1

also im hardly going to fail kk considering im at a b level and im year 10. They made us to practise papers :(

[kk.]

i said n=1 in mine not the whole equation = 1

also im hardly going to fail kk considering im at a b level and im year 10. They made us to practise papers :(

As I said, it didn't help we all had different letters.
I'm only saying that I'm surprised that you haven't been taught it. You can't rely on your calculator or every tiny little sum, you wouldn't finish the paper. I'd advise you to ask your teacher tbh lol

[N!ck]

i said n=1 in mine not the whole equation = 1

also im hardly going to fail kk considering im at a b level and im year 10. They made us to practise papers :(

Well if n = 1 then the odd number that your squaring is 3.

(2n + 1) = 3

So when you do 2(2n^2 + 2n) + 1 with n = 1 you're getting the answer to 3^2.

2[2(1^2) + (2*1)] + 1

= 9