Math Problem

[Nixona]

I've got a stumper math problem...anyone good at this stuff? It's like the second day of class and this one problem is blowin my mind. I just can't grasp it.

Prove that:
1 + r + r² + r³ + ... + rN(power of n) = 1-r N+1 (power of n + 1)/ 1-r

[Epidemic]

simple

just take another major.

Besides I don't have to prove it I will accept it.

I'll let the Communities CAT have a dig.

[lost-and-found]

what math class is this?

[caddmannq]

Start by factoring r out of every term...

Yeah, if that one stumps you...forget Fourier analysis.

<edit for spelling...dang French names ...>

Originally posted by caddmannq
Yeah, if that one stumps you...forget Forrier analysis.

What's that, cadd? Anything like this, maybe?

Cheers
Mick

[caddmannq]

Yep. or this:
http://mathworld.wolfram.com/FourierSeries.html

I spelled it wrong, BTW. It's Fourier. Been so long, I've forgotten.

Used in the study of harmonic analysis. All done by PC now. When I was in school, we didn't have access to computers powerful enough.

[newbie~wan]

caddmann, your EE then right?

Simple algebra really:

1+r+...r**n=r(1/(r+1)+r+...r**(n-1)) - Factor out r as Cadd says.

Divide by (1-r)/(1-r) ---This is effectively 1 so doesn't change anything.

[r(1/(r+1)+r+...r**(n-1))] x (1-r)/(1-r)=

{[r(1/(r+1)+r+...r**(n-1))]-[r+r**2.....+r**(n+1)]}/(1-r)

Above you have just "opened up the brackets and multiplied by 1 and by -r.


={(1+r+r**2....+r**n)-(r+r**2+ .....r**(n+1)}/(1-r)

Cancell all + and - terms above:


{1-r**(n+1)}/(1-r)

QED

[caddmannq]

Geeze, Shahani...
Yer not supposed to give him the whole answer!
How's he gonna learn to factor common terms & multiply by 1?

As you say, simple algebra, but also the basis for everything that follows. If you don't work that stuff out by yourself, you're gonna be totally lost in a week.