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Question

If α is the nth root of unity, then 1+2α+3α2+.... to n terms equal to

A
n(1α)2
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B
n1α
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C
2n1α
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D
2n(1α)2
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Solution

The correct option is B n1α

S=1+2α+3α2+...nαn1
αS=α+2α2+3α3+...(n1)αn1+nαn
S(1α)=1+α+α2+α3+...αn1nαn
S(1α)=1αn1αnαn
Now αn=1 since it is the nth root of unity.
Therefore,
S(1α)=n
S=n1α


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