Question

Tính

B=\(\frac{-1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}-\frac{1}{100000}\)

Answer 1

Ta có : \(B=\frac{-1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}-\frac{1}{100000}\)

\(\Rightarrow B=-\left(\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000}+\frac{1}{100000}\right)\)

Đặt \(A=\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000}+\frac{1}{100000}\)

\(\Rightarrow10A=1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000}\)

\(\Rightarrow10A-A=1-\frac{1}{100000}\)

\(\Rightarrow9A=\frac{99999}{100000}\)

\(\Rightarrow A=\frac{99999}{100000}.\frac{1}{9}=\frac{11111}{100000}\)

=> B = \(-\frac{11111}{100000}\)