2
Question
If ω is an imaginary cube root of unity then expression 1.(2−ω)(2−ω2)+2(3−ω)(3−ω2)+.....+(n−1)(n−ω)(n−ω2) is equal to
If ω is an imaginary cube root of unity then expression 1.(2−ω)(2−ω2)+2(3−ω)(3−ω2)+.....+(n−1)(n−ω)(n−ω2) is equal to
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Solution
The correct option is B 14n2(n+1)2−n
1.(2−w)(2−w2)+2(3−w)(3−w2).......+(n−1)(n−w)(n−w2)using hit and trial method,put n=2 and check for the answer. (2−w)(2−w2) ⇒2(2−w2)−w(2−w2) 4−2w2−2w+w3 5−2(w2+w) 5−2(−1) 5+2 7
1.(2−w)(2−w2)+2(3−w)(3−w2).......+(n−1)(n−w)(n−w2)
using hit and trial method,
put n=2 and check for the answer.
(2−w)(2−w2)
⇒2(2−w2)−w(2−w2)
4−2w2−2w+w3
5−2(w2+w)
5−2(−1)
5+2
7
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