Tính tổng S = (1 + i + i^2 + ...+ i^20)/21. S = 1. S = 1/21

* Hướng dẫn giải

Đáp án B

$$\begin{gathered} \mathrm{Đặt} \mathrm{P}=\mathrm{i}+{\mathrm{i}}^2+...+{\mathrm{i}}^{20} \Rightarrow \mathrm{S}=\frac{1+\mathrm{P}}{21} \\ \mathrm{Ta} \mathrm{thấy} \mathrm{P} \mathrm{là} \mathrm{tổng} \mathrm{của} 1 \mathrm{cấp} \mathrm{số} \mathrm{nhân} \mathrm{với} {\mathrm{U}}_1=\mathrm{i}; {\mathrm{U}}_{20}={\mathrm{i}}^{20} \mathrm{và} \mathrm{công} \mathrm{bội} \mathrm{q}=\mathrm{i} \\ \Rightarrow \mathrm{P}={\mathrm{U}}_1.\frac{1-{\mathrm{q}}^{\mathrm{n}}}{1-\mathrm{q}}=\mathrm{i}.\frac{1-{\mathrm{i}}^{20}}{1-\mathrm{i}} \\ \mathrm{Mặt} \mathrm{khác}: {\mathrm{i}}^{20}={\left({\mathrm{i}}^2\right)}^{10}=1 \\ \Rightarrow \mathrm{P}=\mathrm{i}.\frac{1-1}{1-\mathrm{i}}=0 \\ \Rightarrow \mathrm{S}=\frac{1}{21} \end{gathered}$$