Lời giải:
\(A=\frac{-1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+\frac{1}{3^4}-....+\frac{1}{3^{50}}-\frac{1}{3^{51}}\)
\(3A=-1+\frac{1}{3}-\frac{1}{3^2}+\frac{1}{3^3}-....+\frac{1}{3^{49}}-\frac{1}{3^{50}}\)
\(A+3A=-1-\frac{1}{3^{51}}=-\frac{3^{51}+1}{3^{51}}\)
\(A=-\frac{3^{51}+1}{4.3^{51}}\)