\(-\dfrac{1}{20}-\dfrac{1}{20.19}-\dfrac{1}{19.18}-...-\dfrac{1}{2}.1\)
\(=-\dfrac{1}{20}-\left(\dfrac{1}{20.19}+\dfrac{1}{19.18}+...+\dfrac{1}{2}\right)\)
\(=-\dfrac{1}{20}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-...+\dfrac{1}{18}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{20}\right)\)
\(=-\dfrac{1}{20}-\left(1-\dfrac{1}{20}\right)=-\dfrac{1}{20}-1+\dfrac{1}{20}=-1\)