\(S=\dfrac{2018}{6}+\dfrac{2018}{12}+\dfrac{2018}{20}+......+\dfrac{2018}{2017.2018}\)
\(S=\dfrac{2018}{2.3}+\dfrac{2018}{3.4}+\dfrac{2018}{4.5}+.......+\dfrac{2018}{2017.2018}\)
\(S=2018\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+......+\dfrac{1}{2017.2018}\right)\)
\(S=2018\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+.....+\dfrac{1}{2017}-\dfrac{1}{2018}\right)\)
\(S=2018\left(\dfrac{1}{2}-\dfrac{1}{2018}\right)\)
\(S=2018\cdot\dfrac{504}{1009}\)
\(S=2.504\)
\(S=1008\)
S = \(\dfrac{2018}{6}+\dfrac{2018}{12}+\dfrac{2018}{20}+...+\dfrac{2018}{2017.2018
}\)
S = \(\dfrac{2018}{2.3}+\dfrac{2018}{3.4}+\dfrac{2018}{4.5}+...+\dfrac{2018}{2017.2018}\)
S = \(\dfrac{2018}{2}-\dfrac{2018}{3}+\dfrac{2018}{3}-\dfrac{2018}{4}+...+\dfrac{2018}{2017}-\dfrac{2018}{2018}\)
S = \(\dfrac{2018}{2}-\dfrac{2018}{2018}\)
S = 1009 - 1
S = 1008
