let be the roots of then since we will clearly have: thus:
now let then: which gives us:
but: thus the closed form of your series is:
This is a really confusing question that I haven't been able to solve:
Normally when I post questions, I write down the working that i've done so far (I hate the people who post on here purely for answers and never intend to solve the questions themselves!) but I really have no idea how to start this.Express the power series:
in closed form.
(Hint: Use the fact for the cube root of unity
Since it wants me to use [tex]z^3=1[tex] this will only give me the first three terms. However, since there's an n number of terms would I need the ?
Thanks for that post! I'm understanding parts of it =D
Is this because and are the cube roots of unity? I thought that just was the cube root of unity?
Assuming and are the cube roots of unity, you would also have to include 1 (ie. the cube roots of unity are 1, and . Since the sum of these roots must equal 0 then so ?
How did you end up with this? I've tried working it through on my whiteboard but i'm not ending up with anything like it.
As soon as I know that i'm thinking of it correctly I will probably be able to understand the rest of it.