Question
Mathematics Question on Sequence and series
If ω≠1 is a cube root of unity, then the sum of the series S=1+2ω+3ω2+………+3nω3n−1 is
A
(A) 3n/ω - 1
B
(B) 3n (ω - 1)
C
(C) ω-1/3n
D
(D) 0
Answer
(A) 3n/ω - 1
Explanation
Solution
Explanation:
s=1+2ω+3ω2+………+3nω3n−1sω=ω+2ω2+…………+(3n−1)ω3n+3nω3ns(1−ω)=1+ω+ω2+………+ω3n−1−3nω3k=0−3ns=−3n1−ω=3nω−1