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Vì \(\frac{10^{18}+1}{10^{19}+1}< 1\Rightarrow B=\frac{10^{18}+1}{10^{19}+1}< \frac{10^{18}+1+9}{10^{19}+1+9}\)
\(\Rightarrow B< \frac{10^{18}+10}{10^{19}+10}\)
\(\Rightarrow B< \frac{10\left(10^{17}+1\right)}{10\left(10^{18}+1\right)}\)
\(\Rightarrow B< \frac{10^{17}+1}{10^{18}+1}\)
\(\Rightarrow B< A\)
Vậy A > B.
Ta có: \(A=\frac{-9}{10^{2010}}+\frac{-19}{10^{2011}}=\frac{-9}{10^{2010}}-\frac{9}{10^{2011}}-\frac{10}{10^{2011}}\)
\(=\frac{-9}{10^{2010}}-\frac{9}{10^{1011}}-\frac{1}{10^{2010}}=\frac{-9}{10^{2011}}+\frac{-10}{10^{2010}}\)
Ta thấy : \(\frac{10}{10^{2010}}< \frac{19}{10^{2010}}\Rightarrow\frac{-10}{10^{2010}}>\frac{-19}{10^{2010}}\)
\(\Rightarrow\frac{-9}{10^{2011}}+\frac{-10}{10^{2010}}>\frac{-9}{10^{2011}}+\frac{-19}{10^{2010}}\)
Hay \(A>B\)
Vậy ...
đặt \(A=\frac{10^{18}+1}{10^{19}+1};B=\frac{10^{19}+1}{10^{20}+1}\)
ta có: \(10A=\frac{10^{19}+1+9}{10^{19}+1}=1+\frac{9}{10^{19}+1}\)
\(10B=\frac{10^{20}+1+9}{10^{20}+1}=1+\frac{9}{10^{20}+1}\)
mà \(\frac{9}{10^{19}+1}>\frac{9}{10^{20}+1}\)
=> 10A >10B
=> A > B
\(B=\frac{10^{20}+1}{10^{21}+1}< 1\)
NÊN \(\frac{10^{20}+1}{10^{21}+1}< \frac{10^{20}+1+9}{10^{21}+1+9}=\frac{10^{20}+10}{10^{21}+10}=\frac{10.\left(10^{19}+1\right)}{10.\left(10^{20}+1\right)}=\frac{10^{19}+1}{10^{20}+1}=A\)
VẬY B<A
a ) \(\left(-\frac{40}{51}.0,32.\frac{17}{20}\right):\frac{64}{75}\)
\(=\left(-\frac{40}{51}.\frac{8}{25}.\frac{17}{20}\right):\frac{64}{75}\)
\(=\left(\frac{-40.8.17}{51.25.20}\right):\frac{64}{75}\)
\(=\left(\frac{-16}{75}\right).\frac{75}{64}\)
\(=\frac{-1}{1}.\frac{1}{4}=-\frac{1}{4}\)
Ta có
\(C=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}...+\frac{1}{17.18}>A=\frac{1}{2.3}+\frac{1}{5.4}+...+\frac{1}{18.19}\)
\(C< =>\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{18-17}{17.18}\)\(>A\)
\(C< =>\frac{1}{2}-\frac{1}{18}\)\(>A\)
\(C< =>\frac{4}{9}\)\(>A\left(1\right)\)
Lại có \(C=\frac{4}{9}< \frac{9}{19}=B\left(2\right)\)
Từ (1),(2) => B>A
Ta có: \(A=\frac{10^{18}+1}{10^{19}+1}>\frac{10.\left(10^{17}+1\right)}{10.\left(10^{18}+1\right)}=\frac{10^{17}+1}{10^{18}+1}\)
Vậy A < B
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