A =9^9+1/9^10+1
B=10^9+1/10^10+1
so sanh a va b
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\(A=\frac{-9}{10^{2011}}+\frac{-9}{10^{2010}}\)
\(B=\frac{-9}{10^{2011}}+\frac{-19}{10^{2010}}\)
\(\frac{-9}{10^{2010}}>\frac{-19}{10^{2010}}\)
\(\Rightarrow\frac{-9}{10^{2011}}+\frac{-9}{10^{2010}}>\frac{-9}{10^{2011}}+\frac{-19}{10^{2010}}\)
\(\Rightarrow A>B\)
Ta có: \(A=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{10}\)
\(=1+\left(\frac12+\frac13+\frac16\right)+\left(\frac14+\frac15\right)+\left(\frac17+\frac18+\frac19\right)+\frac{1}{10}\)
\(=1+1+\frac{9}{20}+\frac{1}{10}+\left(\frac17+\frac18+\frac19\right)\)
=2,55+\(\left(\frac17+\frac18+\frac19\right)\) >2,3
=>A>B
\(A< \frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}=\frac{5}{5}=1=B\)
a/
\(\frac{2001}{2004}=\frac{2004-3}{2004}=1-\frac{3}{2004}=1-\frac{1}{668}.\)
\(\frac{39}{40}=\frac{40-1}{40}=1-\frac{1}{40}\)
Ta có \(40< 668\Rightarrow\frac{1}{40}>\frac{1}{668}\Rightarrow1-\frac{1}{40}< 1-\frac{1}{668}\Rightarrow\frac{39}{40}< \frac{2001}{2004}\)
b/
\(A< \frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}=1=B\)
A = 387420490 ; B = 1000000001
vậy B lớn hơn A