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The coefficient of x^(103) in (1+x+x^(2)...

The coefficient of `x^(103)` in `(1+x+x^(2) +x^(3)+x^(4))^(199)(x-1)^(201)` is `"___"`.

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Verified by Experts

The correct Answer is:
0
`E = (1+x+x^(2)+x^(3)+x^(4))^(199) (x-1)^(201)`
`= ((1-x^(5))/(1-x))^(199)(x-1)^(201)`
`= - (1-x)^(2)(1-x^(5))^(199)`
`= - 1(1-2x+x^(2))(1-.^(199)C_(1)x^(5)+.^(199)C_(2)x^(10)-"…..")`
`:.` Coefficient `x^(103)` in `E = 0`
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CENGAGE PUBLICATION-BINOMIAL THEOREM-Numerical
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