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


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


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