$A$=$\dfrac{1}{1×2×3}$+$\dfrac{1}{2×3×4}$+....+ $\dfrac{1}{2014×2015×2016}$
$⇒2A$=$\dfrac{2}{1×2×3}$+$\dfrac{2}{2×3×4}$+...+ $\dfrac{2}{2014×2015×2016}$
$⇒2A$= $\dfrac{1}{1×2}$-$\dfrac{1}{2×3}$+ $\dfrac{1}{2×3}$+..+ $\dfrac{1}{2014×2015}$- $\dfrac{1}{2015×2016}$
$⇒2A$=$\dfrac{1}{2}$- $\dfrac{1}{2015×2016}$
$⇒A$=($\dfrac{1}{2}$- $\dfrac{1}{2015×2016}$)÷2
$⇒A$=$\dfrac{1}{4}$- $\dfrac{1}{2015×2016}$
$⇒A<$ $\dfrac{1}{4}$
$\text{Cho mình câu trả lời hay nhất}$
