Q. In the expansion of $\left(2 x+\frac{1}{2 x}\right)^6$, if the coefficient of $x^2$ is $k$ times the coefficient of $x^{-2}$ then $k$ equals
Binomial Theorem
Solution:
$T _{ r +1}={ }^6 C _{ r }(2 x )^{6- r } \cdot \frac{1}{(2 x )^{ r }}={ }^6 C _{ r } \cdot 2^{6-2 r } \cdot x ^{6-2 r } $
$\text { if } 6-2 r =2 \Rightarrow r =2$
$\text { if } 6-2 r =-2 \Rightarrow r =4$
