Question

In the expansion of ${\left(2x+\frac{1}{2x}\right)}^6$, if the coefficient of $x^2$ is $k$ times the coefficient of $x^{-2}$ then $k$ equals

• A. 4
• B. 8
• C. 16
• D. 32

Answer 1

Answer: (C)

$T_{r+1}={}^6{C}_r(2x{)}^{6-r}\cdot \frac{1}{(2x{)}^r}={}^6{C}_r\cdot 2^{6-2r}\cdot x^{6-2r}$
$\text{ if }6-2r=2\Rightarrow r=2$
$\text{ if }6-2r=-2\Rightarrow r=4$