Question

Tính tổng:A=5/3.9+5/9.15+5/15.21+...+5/63.69

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Answer 1

Ta có : \(A=\frac{5}{3.9}+\frac{5}{9.15}+\frac{5}{5.21}+.....+\frac{5}{63.69}\)

\(\Rightarrow A=\frac{5}{6}\left(\frac{6}{3.9}+\frac{6}{9.15}+\frac{6}{15.21}+......+\frac{6}{63.69}\right)\)

\(\Rightarrow A=\frac{5}{6}\left(\frac{1}{3}-\frac{1}{9}+\frac{1}{9}-\frac{1}{15}+.....+\frac{1}{63}-\frac{1}{69}\right)\)

\(\Rightarrow A=\frac{5}{6}\left(\frac{1}{3}-\frac{1}{69}\right)\)

\(\Rightarrow A=\frac{5}{6}.\frac{22}{69}=\frac{55}{207}\)