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# How to rearrange this expression ?

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1. http://i.imgur.com/Vclwxot.png

I understand what happens do the denominator, but I think the numerator is the wrong way around ?

thanks
2. No the denominator is negative after opening the brackets which results in a fraction that then gets turned upside down to multiply the F.

The - then swaps things round in the numerator to make it look better.
3. (Original post by jon2016)
http://i.imgur.com/Vclwxot.png

I understand what happens do the denominator, but I think the numerator is the wrong way around ?

thanks
Nopes, look at the denominator, it is .

Hence,

But then you swap the numerator to get red of the negative sign, i.e: distribute it.
4. (Original post by ghostwalker)
Looks fine.

Denominator evaluates to minus i/100.

Hence the bit in large square brackets is flipped round.
ah damn I forgot its 1- * ( )
Rather than just 1 -

So denominator equals - i/100

next I multiply it by F ? to get

-100f/i ?

then somehow the negative coefficient of -100f/i goes into the numerator ?
5. (Original post by jon2016)
...
6. (Original post by Zacken)
Nopes, look at the denominator, it is .

Hence,

But then you swap the numerator to get red of the negative sign, i.e: distribute it.
ah thanks clearer know

so the next stage is multiplying the numerator by -1 ?

which gives us -1 + ( )^n

then this can be rearranged as

()^n -1 ? how come you can just swap them like that ?
7. (Original post by jon2016)
ah thanks clearer know

so the next stage is multiplying the numerator by -1 ?

which gives us -1 + ( )^n

then this can be rearranged as

()^n -1 ? how come you can just swap them like that ?
See my above post.
8. (Original post by jon2016)
ah thanks clearer know

so the next stage is multiplying the numerator by -1 ?

which gives us -1 + ( )^n

then this can be rearranged as

()^n -1 ? how come you can just swap them like that ?
Because you are multiply through the bracket by the -1 i.e. -(x^n-1)=-x^n+1=1-x^n

Is that what you are asking?
9. (Original post by nerak99)
Because you are multiply through the bracket by the -1 i.e. -(x^n-1)=-x^n+1=1-x^n

Is that what you are asking?

I was confused because I thought

-1(1 - (1+x)^n) would equal = -1 + (1+x)^n) rather than (1+x)^n) -1 but I guess they are just rearranging it ?

like

-1 + 2 is the same as 2 + -1
10. (Original post by Zacken)

In this example

a= 1 and b = (1+ i/100)^n ?
11. (Original post by jon2016)
In this example

a= 1 and b = (1+ i/100)^n ?
Yep.

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