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If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n),...

If `(1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x_(2n),` find the value of `a_0+a_6++ ,n in Ndot`

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To solve the problem, we need to find the value of \( a_0 + a_3 + a_6 + \ldots \) from the expansion of \( (1 + x + x^2)^n \). ### Step-by-Step Solution: 1. **Understanding the Problem**: We have the expression \( (1 + x + x^2)^n \) which can be expanded using the binomial theorem. The coefficients of the expansion are represented as \( a_0, a_1, a_2, \ldots, a_{2n} \). 2. **Finding \( a_0 + a_1 + a_2 + \ldots + a_{2n} \)**: ...
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