Question

  

Answer 1

\(S=\dfrac{1}{10.12}+\dfrac{1}{12.14}+\dfrac{1}{14.16}+...+\dfrac{1}{2022.2024}\)

\(=\dfrac{1}{2}\left(\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{16}+...+\dfrac{1}{2022}-\dfrac{1}{2024}\right)\)

\(=\dfrac{1}{2}.\left(\dfrac{1}{10}-\dfrac{1}{2024}\right)\)

\(=\dfrac{1}{2}.\dfrac{1007}{10120}\)

\(=\dfrac{1007}{20240}\)

Answer 2

=1/2(2/10*12+2/12*14+...+2/2022*2024)

=1/2(1/10-1/12+1/12-1/14+1/14+...+1/2022-1/2024)

=1/2*1007/10120

=1007/20240