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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: Complex Number
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sachin_gupta1991 (69)

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Q. Prove that [r=1 ][k ]  (-3)r-1  3nC2r-1 = 0 where k=3n/2 and n is even positive
    integer.
    
sachin_gupta1991 (69)

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come on goiitians, try it.....
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nadeemoidu (1184)

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 ( 1 + 3 i) 3n  - ( 1 - 3 i ) 3n = (2w2)3n - (2w) 3n = 2 3n - 2 3n = 0

where w is the cube root of unity.

expand  ( 1 + 3 i) 3n  - ( 1 - 3 i ) 3n  using binomial theorem , divide by 3i and u get the answer.
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