Question

cho a.=\(\frac{2006}{2007}\)+\(\frac{2007}{2008}\)+\(\frac{2008}{2009}\)

so sánh a với 3

júp tớ đi các bạn nếu ko tớ chả biết làm sao nữa

Answer 1

\(\frac{2006}{2007}< \frac{2007}{2007}=1\)

\(\frac{2007}{2008}< \frac{2008}{2008}=1\)

\(\frac{2008}{2009}< \frac{2009}{2009}=1\)

\(\Rightarrow a=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}< 1+1+1=3\)

Answer 2

\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}\)

\(A=\left(1-\frac{1}{2007}\right)+\left(1-\frac{1}{2008}\right)+\left(1-\frac{1}{2009}\right)\)

\(A=\left(1+1+1\right)-\left(\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\right)\)

\(A=3-\left(\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\right)< 3\)