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Mathematics · JEE | BINOMIAL THEOREM
हिन्दीIf \( (1 + x + x^2)^n = a_0 + a_1x + a_2x^2 + \dots + a_{2n}x^{2n} \), then the value of \( a_0 + a_3 + a_6 + a_9 + \dots \) is:
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Correct answer · Option A
\( 3^{n-1} \)
Explanation
Using cube roots of unity \( 1, \omega, \omega^2 \), substitute \( x = 1, \omega, \omega^2 \) into the identity and sum them up to isolate terms with indices divisible by 3, yielding \( \frac{3^n + 0 + 0}{3} = 3^{n-1} \).
