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Algebra

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27 Dec 2007 13:10:27 IST

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Q. Prove that _{[r=1 ]}

^{[k ]} (-3)^r-1 ³ⁿC_2r-1= 0 where k=3n/2 and n is even positive

integer.

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Sachin Gupta

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Joined: 6 Apr 2007

Posts: 146

27 Dec 2007 16:26:50 IST

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come on goiitians, try it.....

Nadeem

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Joined: 25 Aug 2007

Posts: 521

27 Dec 2007 18:23:11 IST

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( 1 +

3 i) ³ⁿ - ( 1 -

3 i )³ⁿ = (2w²)³ⁿ - (2w) 3n = 2³ⁿ - 2³ⁿ = 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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