Given that \(\left( 1+2x \right){{\left( 1-x+{{x}^{2}} \right)}^{10}}={{a}_{0}}+{{a}_{1}}x+{{a}

Question

Given that $\left( 1+2x \right){{\left( 1-x+{{x}^{2}} \right)}^{10}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+\cdots +{{a}_{21}}{{x}^{21}}$, find the value of ${{a}_{2}}+{{a}_{4}}+\cdots +{{a}_{18}}+{{a}_{20}}$.

Accepted Answer

$a_2+a_4+\cdots+a_{20}=-29524$

Binomial Theorem - Sums of Coefficients in Polynomial Expansions

Binomial Theorem - Sums of Coefficients in Polynomial Expansions

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