Question

1. Tính

\(\dfrac{1}{2014}-\dfrac{1}{2014.2013}-\dfrac{1}{2013.2012}-....-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

Answer 1

\(\dfrac{1}{2014}-\dfrac{1}{2014.2013}-\dfrac{1}{2013.2012}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}=\dfrac{1}{2014}-\left(\dfrac{1}{2013.2014}+\dfrac{1}{2012.2013}+....+\dfrac{1}{1.2}\right)=\dfrac{1}{2014}-\left(\dfrac{1}{2013}-\dfrac{1}{2014}+\dfrac{1}{2012}-\dfrac{1}{2013}+...+1-\dfrac{1}{2}\right)=\dfrac{1}{2014}-\left(1-\dfrac{1}{2014}\right)=\dfrac{1}{2014}-\dfrac{2013}{2014}=-\dfrac{2012}{2014}=-\dfrac{1006}{1007}\)

Answer 2

Giúp mình với 

Answer 3

\(\dfrac{1}{2014}-\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}-...-\dfrac{1}{2013\cdot2014}\)

\(=\dfrac{1}{2014}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2013}-\dfrac{1}{2014}\right)\)

\(=\dfrac{1}{2014}-1+\dfrac{1}{2014}=-\dfrac{1006}{1007}\)