Question

6/1.3.5 +6/3.7.9+6/7.9.13+6/9.13.15+6/13.15.19

Answer 1

Giải:

Đặt:

\(A=\dfrac{6}{1.3.7}+\dfrac{6}{3.7.9}+\dfrac{6}{7.9.13}+\dfrac{6}{9.13.15}+\dfrac{6}{13.15.19}\)

\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{8}{1.3.7}+\dfrac{8}{3.7.9}+\dfrac{8}{7.9.13}+\dfrac{8}{9.13.15}+\dfrac{8}{13.15.19}\right)\)

\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{1}{1.3}-\dfrac{1}{3.7}+\dfrac{1}{3.7}-\dfrac{1}{7.9}+\dfrac{1}{7.9}-\dfrac{1}{9.13}+\dfrac{1}{9.13}-\dfrac{1}{13.15}+\dfrac{1}{13.15}-\dfrac{1}{15.19}\right)\)

\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{1}{1.3}-\dfrac{1}{15.19}\right)\)

\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{1}{3}-\dfrac{1}{285}\right)\)

\(\Leftrightarrow A=\dfrac{6}{8}.\dfrac{94}{285}\)

\(\Leftrightarrow A=\dfrac{47}{190}\)

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