Question

[củ lạc giòn tan]

 Tính tổng

A=\(\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{99}}+\frac{7}{10^{100}}\)

Answer 1

[Phạm Tuấn Đạt]

\(A=\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{100}}\)

\(10A=7+\frac{7}{10}+...+\frac{7}{10^{99}}\)

\(\Rightarrow10A-A=9A=7-\frac{7}{10^{100}}\)

Answer 2

[hgf]

Ta có : \(10A=7+\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{99}}\)

                               \(A=\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{99}}+\frac{7}{10^{100}}\)

       \(\Rightarrow9A=10A-A=7-\frac{7}{10^{100}}\)

        \(\Rightarrow A=\frac{7-\frac{7}{10^{100}}}{9}\)