Question

tính S=2011/2012+2012/20113+2013/2014. so sánh S với 3

Answer 1

S=\(\dfrac{2011}{2012}+\dfrac{2012}{2013}+\dfrac{2013}{2014}\)

S=\(\left(1-\dfrac{1}{2012}\right)+\left(1-\dfrac{1}{2013}\right)+\left(1-\dfrac{1}{2014}\right)\)

S=\(\left(1+1+1\right)-\left(\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}\right)\)

S=\(3-\left(\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}\right)\)

\(\Rightarrow S< 3\)