\(A=\dfrac{5}{2\cdot1}+\dfrac{4}{1\cdot11}+\dfrac{3}{11\cdot2}+\dfrac{1}{2\cdot15}+\dfrac{13}{15\times4}\)
\(A\cdot\dfrac{1}{7}=\dfrac{5}{2\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{3}{11\cdot14}+\dfrac{1}{14\cdot15}+\dfrac{13}{15\cdot28}\)
\(A\cdot\dfrac{1}{7}=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{28}\)
\(A\cdot\dfrac{1}{7}=\dfrac{1}{2}-\dfrac{1}{28}\)
\(A\cdot\dfrac{1}{7}=\dfrac{13}{28}\)
\(A=\dfrac{13}{4}\)
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