\(A=\dfrac{1}{168}+\dfrac{1}{224}+\dfrac{1}{288}+\dfrac{1}{360}+\dfrac{1}{440}\)
\(A=\dfrac{1}{12\cdot14}+\dfrac{1}{14\cdot16}+\dfrac{1}{16\cdot18}+\dfrac{1}{18\cdot20}+\dfrac{1}{20\cdot22}\)
\(A=\dfrac{1}{2}\cdot\left(\dfrac{1}{12}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{22}\right)\)
\(A=\dfrac{1}{2}\cdot\left(\dfrac{1}{12}-\dfrac{1}{22}\right)\)
\(A=\dfrac{1}{2}\cdot\left(\dfrac{22}{264}-\dfrac{12}{264}\right)\)
\(A=\dfrac{1}{2}\cdot\dfrac{10}{264}\)
\(A=\dfrac{1}{2}\cdot\dfrac{5}{132}\Rightarrow A=\dfrac{5}{264}\)
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