A) 0
B) n
C) ? n
D) 2n
Correct Answer: C
Solution :
Let us take \[{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{2n}}{{x}^{2n}}={{(1+x+{{x}^{2}})}^{n}}\] Differentiating with respect to x on both sides \[{{a}_{1}}+2{{a}_{2}}x+...+2n\,{{a}_{2n}}{{x}^{2n-1}}\] = \[n{{(1+x+{{x}^{2}})}^{n-1}}(2x+1)\] Put x = ? 1Þ \[{{a}_{1}}-2{{a}_{2}}+3{{a}_{3}}-....+2n\,{{a}_{2n}}=-n\].You need to login to perform this action.
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