A) 3
B) 6
C) 9
D) 12
E) 15
Correct Answer: A
Solution :
\[{{(1+x+{{x}^{2}})}^{-3}}={{\left[ \frac{1}{(1+x+{{x}^{2}})} \right]}^{3}}\] \[={{\left[ \frac{1-x}{1-{{x}^{3}}} \right]}^{3}}\] \[={{(1-x)}^{3}}{{(1-{{x}^{3}})}^{-3}}\] \[=(1-{{x}^{3}}-3{{x}^{2}}+3x)(1+3{{x}^{3}}+6{{x}^{6}}+.....)\] \[\therefore \]Coefficient of\[{{x}^{6}}\]in\[{{(1+x+{{x}^{2}})}^{-3}}\] \[=6-3=3\]
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