Question

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

• A. $99$
• B. $403$
• C. $-97$
• D. $51$

Answer 1

Answer: (C)

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