HOC24
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x + 5 = 98
x = 98 - 5
x = 93
\(D=\frac{\left(2!\right)^2}{1^2}+\frac{\left(2!\right)^2}{3^2}+\frac{\left(2!\right)^2}{5^2}+\frac{\left(2!\right)^2}{7^2}+...+\frac{\left(2!\right)^2}{2015^2}\)
=>\(D=\frac{\left(1.2\right)^2}{1^2}+\frac{\left(1.2\right)^2}{3^2}+\frac{\left(1.2\right)^2}{5^2}+\frac{\left(1.2\right)^2}{7^2}+...+\frac{\left(1.2\right)^2}{2015^2}\)
=>\(D=\frac{2^2}{1^2}+\frac{2^2}{3^2}+\frac{2^2}{5^2}+\frac{2^2}{7^2}+...+\frac{2^2}{2015^2}\)
=>\(D=2\left(\frac{2}{1^2}+\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2015^2}\right)\)
Ta có: \(\frac{2}{1^2}+\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2015^2}< 2+\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\)
=>\(D=2\left(\frac{2}{1^2}+\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2015^2}\right)< 2\left(2+\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)
Mà \(2\left(2+\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)\(=2\left(2+\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=2\left(2+1-\frac{1}{2015}\right)=2\left(3-\frac{1}{2015}\right)=6-\frac{6}{2016}< 6\)
=>\(D< 2\left(2+\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)< 6\)
=>D<6
\(\frac{2005}{2006}\)
\(\frac{200520052005}{200720072007}\)
\(Do2006< 200720072007\Rightarrow\frac{2005}{2006}>\frac{200520052005}{200720072007}\)