tính nhanh:
-1/10-1/100-1/1000-1/10000-1/100000
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10C=1-1/10-1/100-1/1000-1/10000-1/100000
10C-C=(1-1/10-1/100-1/1000-1/10000-1/100000)-(1/10-1/100-1/1000-1/10000-1/100000-1/000000)
9C=1-1/10-1/10+1/1000000=800001/1000000
C=800001/1000000:9=88889/1000000
B = \(-\frac{1}{10}-\frac{1}{100}-\frac{1}{1000}-...-\frac{1}{1000000}\)
B = \(-\left(\frac{1}{10}+\frac{1}{10^2}+\frac{1}{10^3}+...+\frac{1}{10^6}\right)\)
Đặt A = \(\frac{1}{10}+\frac{1}{10^2}+\frac{1}{10^3}+...+\frac{1}{10^6}\)
10A = \(1+\frac{1}{10}+\frac{1}{10^2}+...+\frac{1}{10^5}\)
9A = 10A - A = \(1-\frac{1}{10^6}\)
=> A = \(\frac{1-\frac{1}{10^6}}{9}\)
=> B = \(-\left(\frac{1-\frac{1}{10^6}}{9}\right)\)
C=(0,1+0,01+0,001+...+0,000001)=-0,111111
mình ko chép đề bài
\(C=-\frac{1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}-\frac{1}{100000}\)
\(10C=-1-\frac{1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}\)
\(10C-C=\left(-1-\frac{1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}\right)-\left(\frac{-1}{10}-\frac{1}{100}-...-\frac{1}{100000}\right)\)
\(9C=-1+\frac{1}{100000}\)
\(C=\frac{\frac{1}{100000}-1}{9}\)
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 = \(-\frac{11111}{100000}\)
\(A=\frac{-1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}-\frac{1}{100000}\)
\(\Rightarrow A=-\left(\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000}+\frac{1}{100000}\right)\)
\(\Rightarrow A=-\left(\frac{10000}{100000}+\frac{1000}{100000}+\frac{100}{100000}+\frac{10}{100000}+\frac{1}{100000}\right)\)
\(\Rightarrow A=-\left(\frac{10000+1000+100+10+1}{100000}\right)\)
\(\Rightarrow A=-\left(\frac{11111}{100000}\right)\)
\(\Rightarrow A=\frac{-11111}{100000}\)
ta có:
\(- \frac{1}{10} - \frac{1}{100} - \frac{1}{1000} - \frac{1}{10000} - \frac{1}{100000}\)
= \(- \left(\right. 0 , 1 + 0 , 01 + 0 , 001 + 0 , 0001 + 0 , 00001 \left.\right)\)
= \(- 0 , 11111\)
=-0,11111