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  • The coefficient of  in the following expansion, <img alt="\small \sum_{m=0}^{100}{

The coefficient of \small x^{53} in the following expansion, \small \sum_{m=0}^{100}{ }^{100} C_m(x-3)^{100-m} \cdot 2^m  is

Option: 1

{ }^{100} \mathrm{C}_{47}


Option: 2

{ }^{100} C_{53}


Option: 3

{ }^{-100} C_{53}


Option: 4

{ }^{-100} C_{100}


Answers (1)

best_answer

The given sigma is expansion of  [(x-3)+2]^{100}=(x-1)^{100}=(1-x)^{100}

\therefore x^{53} \text { will occur in } T_{54}

T_{54}={ }^{100} C_{53}(-x)^{53}

\therefore \text{Coefficient is}\ -{ }^{100} \mathrm{C}_{53}.
 

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Sayak

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