A) 4
B) 8
C) 12
D) None of these
Correct Answer: D
Solution :
\[{{\left( \frac{1-x}{1+x} \right)}^{2}}={{(1-x)}^{2}}{{(1+x)}^{-2}}\] \[=(1-2x+{{x}^{2}})[1+(-2)x+\frac{(-2)(-2-1)}{2!}{{x}^{2}}\] \[+\frac{(-2)(-2-1)(-2-2)}{3!}{{x}^{3}}+...]\] \[=(1-2x+{{x}^{2}})(1-2x+3{{x}^{2}}-4{{x}^{3}}+5{{x}^{4}}-...)\] \[\therefore \]Coefficient of\[{{x}^{4}}\]in the expansion of\[{{\left( \frac{1-x}{1+x} \right)}^{2}}\] \[=5+(-2)(-4)+(1)(3)\] \[=5+8+3=16\]
You need to login to perform this action.
You will be redirected in
3 sec
