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HSC 2013 MX2 Marathon (archive) (1 Viewer)

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Carrotsticks

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Re: HSC 2013 4U Marathon

I i'm wondering, shouldn't this be <3? because that never reaches 3?

Are you allowed to say =3?
The expression on the right is an infinite series, which is EQUAL to 3.

If I took a partial sum that added a finite number (say N) of terms, then you could say it's less than 3.

Kinda the same reason why 0.99999..... = 1, contrary to popular belief that 0.999999...... < 1.
 

Menomaths

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Re: HSC 2013 4U Marathon

I i'm wondering, shouldn't this be <3? because that never reaches 3?

Are you allowed to say =3?
Let x=0.9999999.....
10x = 9.99999999....
10x-x = 9 since the 9's cancel each other
9x = 9
x = 1
Therefore 1 = 0.999999.....
Yay for first contribution to 4U marathon
 

AnimeX

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Re: HSC 2013 4U Marathon

The expression on the right is an infinite series, which is EQUAL to 3.

If I took a partial sum that added a finite number (say N) of terms, then you could say it's less than 3.

Kinda the same reason why 0.99999..... = 1, contrary to popular belief that 0.999999...... < 1.
Not quite getting this.

So does that mean this is wrong? (changing the places of < sign and = sign)

 

Carrotsticks

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Re: HSC 2013 4U Marathon

I'll short-name it as L, M and R.

It should be L < M = R.

So L is less than M, but M is equal to R, so therefore L is less than R.
 

RealiseNothing

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Re: HSC 2013 4U Marathon

Not quite getting this.

So does that mean this is wrong? (changing the places of < sign and = sign)



I took each term, and made it correspond to a slightly larger term so I could establish an upper bound for the series:





etc

So you end up with my result.
 

Tmalak

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Re: HSC 2013 4U Marathon

2013 Trials PLEASEtrollface.jpg
 

HeroicPandas

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Re: HSC 2013 4U Marathon





i stuffed up the latex typing lol

i thought of another method: (does it work?)

 
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Re: HSC 2013 4U Marathon

As I said...just use the align or eqnarray function...~~~~~~ is a manual function that is the antithesis of LaTeX.
 

Sy123

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Re: HSC 2013 4U Marathon

Yep HeroicPandas, that's pretty much it, that is 7 marks from a school trial (ascham 2005)

===





 
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