Question

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

GIÚP MÌNH NHA CHIỀU MÌNH NỘP RÙI

Answer 1

 

A=−13+132−133+...+1350−1351

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

\(\Rightarrow3A+A=-1+\frac{1}{3}-\frac{1}{3^2}+....+\frac{1}{3^{49}}-\frac{1}{3^{50}}+\left(-\frac{1}{3}+.....-\frac{1}{3^{51}}\right)\)

\(\Rightarrow4A=-1-\frac{1}{3^{51}}\)

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