Tính tổng $\displaystyle S=1+\frac{2}{3}+\frac{4}{9}+\cdots +\frac{{{2}^{n}}}{{{3}^{n}}}+\cdots $. A. $\displaystyle S=3.$ B. $S=4.$ C. $S=5.$ D. $S=6.$
Đáp án đúng: A Ta có $\displaystyle S=1+\frac{2}{3}+\frac{4}{9}+\cdots +\frac{{{2}^{n}}}{{{3}^{n}}}+\cdots =\underbrace{1+\frac{2}{3}+{{\left( \frac{2}{3} \right)}^{2}}+\cdots +{{\left( \frac{2}{3} \right)}^{n}}+\cdots }_{CSN\,\,lvh:\,\,\,{{u}_{1}}=1,\,\,q=\frac{2}{3}}=\frac{1}{1-\frac{2}{3}}=3.$ Chọn A.