Tìm giá trị nhỏ nhất của các biểu thức -4|2.8-s|và 11/5-|s+9|

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

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

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

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

\(=-\frac{11111}{10000}=-1,1111\)

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

\(=-\left(\frac{10000}{10000}+\frac{1000}{10000}+\frac{100}{10000}+\frac{1}{10000}\right)\)

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

\(=-\left(\frac{11111}{10000}\right)\)

Vậy.....

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 = \(-\frac{11111}{100000}\)

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

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

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

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

\(\Rightarrow A=-\left(\frac{11111}{100000}\right)\)

\(\Rightarrow A=\frac{-11111}{100000}\)

mình cũng có câu hỏi giống bạn mà chả thấy câu trả lời

\(-1-\left(\frac{1}{10}\right)-\frac{1}{100}-\frac{1}{1000}+\frac{1}{10000}\)

\(=1,1111\)

88889/1000000=0.088889

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

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

\(10C-C=\left(-1-\frac{1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}\right)-\left(\frac{-1}{10}-\frac{1}{100}-...-\frac{1}{100000}\right)\)

\(9C=-1+\frac{1}{100000}\)

\(C=\frac{\frac{1}{100000}-1}{9}\)

cảm ơn bạn nhiều lắm Bonking mai mình cần nếu bạn giúp được mình có câu hổi mới đăng bạn giúp mình được ko

a) \(A=\left(-1\right)^{2n}.\left(-1\right)^n.\left(-1\right)^{n+1}=\left(-1\right)^{3n+1}\)

b) \(B=\left(10000-1^2\right)\left(10000-2^2\right).........\left(10000-1000^2\right)\)

\(=\left(10000-1^2\right)\left(10000-2^2\right)......\left(10000-100^2\right)....\left(10000-1000^2\right)\)

\(=\left(10000-1^2\right)\left(10000-2^2\right).....\left(10000-10000\right).....\left(10000-1000^2\right)=0\)

c) \(C=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)..........\left(\frac{1}{125}-\frac{1}{25^3}\right)\)

\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right).....\left(\frac{1}{125}-\frac{1}{5^3}\right)......\left(\frac{1}{125}-\frac{1}{25^3}\right)\)

\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)........\left(\frac{1}{125}-\frac{1}{125}\right).....\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)

d) \(D=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-10^3\right)}\)

\(=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-1000\right)}=1999^0=1\)