Chứng minh E <2

M

minhhieupy2000

Ta có: $ \dfrac16+\dfrac17+\dfrac18 < 3\dfrac16=\dfrac12$
$\dfrac19+\dfrac1{10}+\dfrac1{11}< 3\dfrac1{9}=\dfrac13$
$\dfrac1{12}+\dfrac1{13}+\dfrac1{14} < 3\dfrac1{12}=\dfrac14$
$\dfrac1{15}+\dfrac1{16}+\dfrac1{17} < 3\dfrac1{15}=\dfrac15$


\Rightarrow $\dfrac12+...+\dfrac1{16}+\dfrac1{17}<2(\dfrac12+ \dfrac13 +\dfrac14+\dfrac15 )< 2(\dfrac12+\dfrac12+\dfrac14+\dfrac14)=3$
\Rightarrow $\dfrac15+...+\dfrac1{16}+\dfrac1{17} < 3-\dfrac12-\dfrac13-\dfrac14<2$
\Rightarrow đpcm
 
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