\(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+...+\dfrac{1}{121\times123}\)
\(=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{121}-\dfrac{1}{123}\right)\)
\(=\dfrac{1}{2}.\left(1-\dfrac{1}{123}\right)\)
\(=\dfrac{1}{2}.\left(\dfrac{123}{123}-\dfrac{1}{123}\right)\)
\(=\dfrac{1}{2}.\dfrac{122}{123}\)
\(=\dfrac{61}{123}\)
\(#NqHahh\)