Question

tính: \(-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{^{3^3}}+.....+\frac{1}{3^{50}}-\frac{1}{3^{51}}\)

Answer 1

Đặt \(A=-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{50}}-\frac{1}{3^{51}}\)

\(\Rightarrow3A=-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{49}}-\frac{1}{3^{50}}\)

\(\Rightarrow A+3A=\left(-\frac{1}{3}+\frac{1}{3^2}-...-\frac{1}{3^{51}}\right)+\left(-1+\frac{1}{3}-...-\frac{1}{3^{50}}\right)\)

\(\Leftrightarrow4A=-1-\frac{1}{3^{51}}\)

\(\Leftrightarrow4A=-\frac{3^{51}+1}{3^{51}}\Rightarrow A=-\frac{3^{51}+1}{3^{51}.4}\)

Answer 2

cảm ơn bạn Tuấn Anh nhiều nhé