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\(B=10^{10}-10^9-10^8=10^8\left(100-10-1\right)=10^8.89⋮89\)
\(\Rightarrow B⋮89\)
`Answer:`
Đặt \(N=\frac{9}{10}+\frac{9}{10^2}+\frac{9}{10^3}+...+\frac{9}{10^{10}}\)
\(\Rightarrow\frac{N}{9}=\frac{1}{10}+\frac{1}{10^2}+\frac{1}{10^3}+...+\frac{1}{10^{10}}\)
Ta có \(\frac{N}{90}=\frac{1}{10^2}+\frac{1}{10^3}+\frac{1}{10^4}+...+\frac{1}{10^{11}}\)
\(\Rightarrow\frac{N}{9}-\frac{N}{90}=\left(\frac{1}{10}+\frac{1}{10^2}+\frac{1}{10^3}+...+\frac{1}{10^{10}}\right)-\left(\frac{1}{10^2}+\frac{1}{10^3}+\frac{1}{10^4}+...+\frac{1}{10^{11}}\right)\)
\(\Rightarrow\frac{10N}{90}-\frac{N}{90}=\frac{1}{10}+\frac{1}{10^2}+\frac{1}{10^3}+...+\frac{1}{10^{10}}-\frac{1}{10^2}-\frac{1}{10^3}-\frac{1}{10^4}-...-\frac{1}{10^{11}}\)
\(\Rightarrow\frac{9N}{90}=\frac{1}{10}-\frac{1}{10^{11}}\)
\(\Rightarrow\frac{N}{10}=\frac{10^{10}-1}{10^{11}}\)
\(\Rightarrow N=\frac{10^{10}-1}{10^{10}}\)
Tính
a) \(\dfrac{1}{2}\) . ( \(\dfrac{4}{3}\) + \(\dfrac{2}{5}\) ) - \(\dfrac{3}{4}\) . ( \(\dfrac{8}{9}\) + \(\dfrac{13}{3}\) )
= \(\dfrac{1}{2}\) . \(\dfrac{8}{15}\) - \(\dfrac{3}{4}\) . \(\dfrac{47}{9}\)
= \(\dfrac{4}{15}\) - \(\dfrac{47}{12}\)
= \(\dfrac{-73}{20}\)
b) \(\dfrac{1}{5}\) : \(\dfrac{1}{10}\) - \(\dfrac{1}{3}\) . ( \(\dfrac{6}{5}\)-\(\dfrac{9}{4}\) )
= 2 - \(\dfrac{1}{3}\) . \(\dfrac{-21}{20}\)
= 2 - \(\dfrac{-7}{20}\)
= \(\dfrac{47}{20}\)
c) \(\dfrac{-3}{4}\) . ( \(\dfrac{20}{9}\) - \(\dfrac{8}{15}\) ) - \(\dfrac{5}{3}\) . \(\dfrac{9}{10}\)
= \(\dfrac{-3}{4}\) . \(\dfrac{76}{45}\) - \(\dfrac{3}{2}\)
= \(\dfrac{-19}{15}\) - \(\dfrac{3}{2}\)
= \(\dfrac{-7}{30}\)
9 + 10 + 9 + 10 +9 +10 + 9 +10 + M + C + M
= 9 + 10 + 9 + 10 +9 +10 + 9 +10 + 1000 + 100 + 1000
= 2176
9 + 10 + 9 + 10 +9 +10 + 9 +10 + M + C + M
= 9 + 10 + 9 + 10 +9 +10 + 9 +10 + 1000 + 100 + 1000
9 x 4+ 10 x 4 + 1000 x 2 +100
= 2176