# Maths Question Driving Me Insane

#### dyserq

##### Fully Optimized
Hi people
I know this may sound unreasonable making a new thread for this but this is really annoying me ... i really am ticked off because everybody has different answers about it ...
Anyhow, i had my yearly maths exam today ... which is primarily the reason as to why i haven't been on much all of a sudden ... i also have 3 more yearly exams coming up ...
Well ... this is the question ... i personally put 1,000,000 as the answer to this question ... i'm pretty sure that it is but there are like a different answer for every person that i ask

Find n
1 = 1Â² = 1
1 + 3 = 2Â² = 4
1 + 3 + 5 = 3Â² = 9
1 + 3 + 5 + ... + 1999 = nÂ² = n

This is probably pretty basic for you ... but everybody at my school is finding it a weird one ... could anybody please help ?

#### UK31337

##### Fully Optimized
Looks like the binomial series. I covered it a couple of weeks ago, but I didn't understand to do just what you're asking, I'm afraid I can expand an expression like (x+y)^4, but no more than that.

#### dyserq

##### Fully Optimized
Well thanks anyways #### eTech|Stacy

##### Baseband Member
You could also consider this Logic:

(first no+last no)/2 sqr
=((1+1999)/2) sqr= 1000 sqr

Calculate this and you will get your solution. #### root

##### Site Team
Staff member
OK...

firstly that question is wrong, n^2 != n (but we'll ignore that unless you want to but some cheecky remarks in your book, the only time n^2 = 1 is when n=1).

the sequence is 1+3+5... + k-2 + k = n^2
n = k/2+.5

eg, 1 = 1^2 -> 1 = 1/2 + .5 = 1 (correct)
1+3 = 2^2 -> 3/2 + .5 = 2 (correct)
1+3+5 = 3^2 -> 5/2 + .5 = 3 (correct)

1+2+3+...+1999 = 1999 / 2 + .5 = 500,

n=500 and n^2 = 250,000

<edit>
dammit, beaten to it, thats what happens when you answer the phone and have to explain how to share email folders!!!

<edit again>
actually not beaten to it,
like I said, the question is badly written, either me or stacy are squaring the wrong number
this comes frmo the way it's written, n=n^2

dosey maths teachers.

#### dyserq

##### Fully Optimized
Wow ... thanks heaps eTech|Stacy and root This will be EXTREMELY helpful and i can not thank you enough ...
And yes ... maybe i should complain to the teachers about how wrong their equation wrong ... i thought there was something funny about that Thanks heaps again !

#### lhuser

##### Golden Master
dyserq said:
Find n
1 = 1Â² = 1
1 + 3 = 2Â² = 4
1 + 3 + 5 = 3Â² = 9
1 + 3 + 5 + x + 1999 = nÂ² = n
Looks like Pythagorean theorem...

#### dyserq

##### Fully Optimized
lhuser said:
Looks like Pythagorean theorem...
Uhh ... Pythagora's Theoram is aÂ²+bÂ²=cÂ² ...

#### lhuser

##### Golden Master
I know. It looks like...oh...I meant it is similar...

#### catalyst1

##### BSOD
Yeah, I noticed that, too. I was like.... wait, n^2 = n?????? WTF? Which n do they want? But yeah, Stacey has it right. The first n would be 1000, and the second n would be 1,000,000 (one million). Root - your logic is correct, but you messed up a bit on your math. 1999/2 + 0.5 = 1000, not 500. Anyway, you guys are basically doing the same thing, just in a different order. Stacy's method is probably a bit easier, but they both work out the same way.