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Coefficient of \mathrm{x}^{2009} \text { in }\left(1+\mathrm{x}+\mathrm{x}^2+\mathrm{x}^3+\mathrm{x}^4\right)^{1001}(1-\mathrm{x})^{1002} \text { is }

 

Option: 1

0


Option: 2

\text { }{ }^{10001} \mathrm{C}_{501}


Option: 3

-2009


Option: 4

none of these


Answers (1)

best_answer

\left(1+x+x^2+x^3+x^4\right)^{1001}(1-x)^{1002}=(1-x)\left(1-x^5\right)^{1001}so all the powers of x will be of the 5m or 5m + 1 form (m∈I)  So coeff. of x2009 will be 0 .

 

Posted by

Pankaj Sanodiya

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