Question

Tính giá trị biểu thức 1/3+1/3mu2+1/3mu3+....+1/3mu2017

Answer 1

\(S=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{2017}}\)

\(3S=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{2016}}\)

\(3S-S=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{2016}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{2017}}\right)\)

\(2S=1-\frac{1}{3^{2017}}\)

\(\Rightarrow S=\frac{1-\frac{1}{3^{2017}}}{2}\)