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Let N=""^(2000)C1+2 .""^(2000)C2+3 .""^(...

Let `N=""^(2000)C_1+2 .""^(2000)C_2+3 .""^(2000)C_(3)+....+2000.""^(2000)C_(2000)`.Prove that N is divisible by `2^(2003)`

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