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  4. The coefficient of x50 in the expansion of ((3-5x)/(1-x)2) equals

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Q. The coefficient of $x^{50}$ in the expansion of $\frac{\left(3-5x\right)}{\left(1-x\right)^{2}}$ equals

Binomial Theorem

Solution:

$\frac{3-5x}{\left(1-x\right)^{2}} = \left(3-5x\right) \left(1-x\right)^{-2}$
$= \left(3 - 5x\right) \left(1 + 2x + 3x^{2 }+ ... + 50x^{49} + 51x^{50} +...\right)$
$\therefore $ Required coefficient $= 3 \times 5 1 - 5 \times 50$
$= 153 - 250 = - 97$