complex no series

i am getting

s=n/(w-1)

Does this have something to do with differentiation? Cos i notice that it is f'(ω) where f(x)=c+x+x²+x³+........+xⁿ.[7]

Yes. I'm noticing that now. but at first sight, the only thing that came to me was differentiation. But I didn't know the alternative expression for f(x).

S= 1+2ω+3ω²+...............nω^n-1

ωS= ω+2ω²+............+n-1ω^n-1+nωⁿ

S-Sω= 1+ω+ω²+...........+ω^n-1-nωⁿ

S=(1-ωⁿ)/(1-ω)² - nωⁿ/(1-ω)

=(1-ωⁿ-nωⁿ+nωⁿ⁺¹)/(1-ω)²
=[1-(n+1)ωⁿ+nωⁿ⁺¹]/(1-ω)²
Is this anywhere near the answer? [2]

nishant,aragorn, thanks for the solution

@ Aragorn,you got the answer

S-Sω= 1+ω+ω²+...........+ω^n-1-nωⁿ
=-nωⁿ (as 1+ω+ω²+...........+ω^n-1=0)

S= n/(ω-1)

Oh! Ok [1]

Can anyone pls give me the proof for 1+ω+ω²+.........+ω^n-1=0?

1+ω+ ω² + .... = (1-ωⁿ)/(1-ω) =(1-1)/(1-ω)= 0

for aragorn for a polynomial sum of roots is coff of -x^n-1/coeff of xⁿ

But here co-eff of -x^n-1 is 0. So sum is 0? Thanx machan [1]