2010/2+2010/6+2010/12+...2010/9900
=2010/1x2+2010/2x3+.....+2010/99x100
=1-1/2+1/2-1/3+......+1/99-1/100
=1-1/100=99/100
2,2^x+2-2^x=96
2^x(4-1)=96
2^x=96:3=32
-> x=5
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Ta có: \(\dfrac{2010}{2}+\dfrac{2010}{6}+\dfrac{2012}{12}+...+\dfrac{2010}{9900}\)
\(=2010\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}\right)\)
\(=2010\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(=2010\left(1-\dfrac{1}{100}\right)\)
\(=2010\cdot\dfrac{99}{100}=\dfrac{19899}{10}\)
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