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)

$-97$

Answer 2

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