\(4S=\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+\dfrac{4}{13\times17}+...+\dfrac{1}{41\times45}\\ 4S=\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}+...+\dfrac{1}{41}-\dfrac{1}{45}\\ 4S=\dfrac{1}{5}-\dfrac{1}{45}\\ 4S=\dfrac{8}{45}\\ S=\dfrac{8}{45}\div4\\ S=\dfrac{2}{45}\)