2unit Question 10; Limiting sums. (1 Viewer)

[Graceofgod]

its a pretty complicated reasoning as to why this works - which you wont prove till some math courses on real analysis. there is however a theorem which states that we can differentiate or integrate each term of the series like a normal polynomial of a power series (i know its wiki but just look at the form of a power series).

1 + x^2 + x^3 + ... = 1/(1 - x) is in this form, thus our theorem allows us to integrate or differentiate each term and equate it to the derivative or integral of the RHS

d/dx(1) + d/dx(x^2) + d/dx(x^3) + ... + d/dx(x^n) + ... = d/dx[1/(1 - x)]

1 + 2x + 3x^2 + ... + nx^(n-1) + ... = 1/(1 - x)^2

I see, however:

d/dx[1/(1 - x)] = -(1/(1-x)^2)

 

[trailblazer]

Nothing is wrong with dota. Just when people with pudge in their avatar play it... =S

Whats your ba name? I will play you after hsc.

Why not now? I have the HSC too.

 

[Graceofgod]

you're forgetting to multiply by the derivative of (1 - x)

Oh yeah, of course. Sorry not looking properly, had a bad day.

But thanks, I never knew you could do that. Makes my awesome question somewhat less awesome.

 

[Graceofgod]

Why not now? I have the HSC too.

I deleted it off my computer during hsc ^.^

Too tempting.

 

[loler]

wtf who the hell is going to realise dat. my head is spinning just trying to work it out
nice question but

 

[lyounamu]

wtf who the hell is going to realise dat. my head is spinning just trying to work it out
nice question but

It's not a rocket science. It's pretty easy once you try to get a bigger picture.