(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let w = e^((2pi*i)/n). Show that 1+2w+3w^2+......+nw^(n-1) = n/(w-1)

2. Relevant equations

1+x+x^2+x^3+....+x^m = (1-x^(m+1))/(1-x) --> A

1+x+x^2+x^3+.... = 1/(1-x) --> B

3. The attempt at a solution

First of all, multiply (w-1) on both sides, then we get

w+2w^2+3w^3+...+(nw^n)-1-2w-3w^3-...-nw^(n-1) = n we simplify left side,

-1-w-w^2-w^3-...-w^n+(nw^n) = n add -1 on both sides

1+w+w^2+w^3+...+w^n-(nw^n) = -n

1+w+w^2+w^3+...+w^n = (nw^n)-n for the left side, we know from A that

(1-w^(n+1))/(1-w) = (nw^n)-n

But I can't get left side and right side equal.

Did I use the right method? Which part is wrong?

Please tell me...

Thank you

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex variables

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**