Question

The coefficient of $x^5$ in the expansion of $\frac{1+x^2}{1+x}$, $\left|x\right|<1$

• A. -1
• B. 2
• C. 0
• D. -2

Answer 1

The correct option is D -2

$(1+x^2)(1+x{)}^{-1}$
$=(1+x^2)(1-x+x^2-x^3..\infty )$
$=(1-x+x^2-x^3..\infty )+x^2(1-x+x^2-x^3..\infty )$
Hence the coefficient of $x^5$ is
$=-1+(-1)$
$=-2$