Question

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

• A. 99
• B. 403
• C. -95
• D. 51

Answer 1

The correct option is C -95

Given, $(3-5x)(1-x{)}^{-2}$
$=(3-5x)(1+2x+3x^2+4x^3...50x^{49}+51x^{50}...\infty )$
Hence coefficient of $x^{50}$
$=3\left(51\right)-5\left(50\right)$
$=155-250$
$=-95$