Khai triển (1+x+x^2+x^3)^10=a0+a1x+...+a30.x^30. Tính tổng

* Hướng dẫn giải

Đáp án B

Ta có: ${\left[{\left(1+x+x^2-x^3\right)}^{10}\right]}^{\text{'}}=\left(a_0+a_{1}x+\mathrm{...}+a_{30}{x}^{30}\right)$

${}^{\text{'}}\iff 10{\left(1+x+x^2-x^3\right)}^9\left(1+x+x^2-x^3\right)$

$$\begin{gathered} a_1+2a_{2}x+\mathrm{...}+30a_{30}{x}^{29} \\ \iff 10{\left(1+x+x^2-x^3\right)}^9{a}_1+2a_{2}x+\mathrm{...}+30a_{30}{x}^{29} \end{gathered}$$

Chọn:  $x=1\Rightarrow 10{\left(1+1+1-1\right)}^9.0=a_1+2a_{2}x+\mathrm{...}+30a_{30}$

$\iff S=0$