Chủ đề này có 2 trả lời

[hakimanh1]

Toán lớp 6 ạ

1. Cho $A=\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}
, B= \frac{2008+2009+2010}{2009+2010+2011}$

So sánh A và B.

2. Chứng minh:$\frac{3}{5}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{60}<\frac{4}{5}$

[Ngoc Hung]

1) Ta có $\frac{2008}{2009}> \frac{2008}{2009+2010+2011}$

$\frac{2009}{2010}> \frac{2009}{2009+2010+2011}$

$\frac{2010}{2011}> \frac{2010}{2009+2010+2011}$

Cộng theo vế được A > B

2) $\left ( \frac{1}{31}+...+\frac{1}{40} \right )+\left ( \frac{1}{41}+...+\frac{1}{50} \right )+\left ( \frac{1}{51}+...+\frac{1}{60} \right )< \frac{10}{30}+\frac{10}{40}+\frac{10}{50}=\frac{47}{60}< \frac{48}{60}=\frac{4}{5}$

Ta lại có $\left ( \frac{1}{31}+...+\frac{1}{40} \right )+\left ( \frac{1}{41}+...+\frac{1}{50} \right )+\left ( \frac{1}{51}+...+\frac{1}{60} \right )> \frac{10}{40}+\frac{10}{50}+\frac{10}{60}=\frac{37}{60}> \frac{36}{60}=\frac{3}{5}$

[hakimanh1]

Thank