Question

Tính:D=1/3.5+1/5.7+1/7.9+...+1/29.31

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Answer 1

\(D=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+......+\frac{1}{29.31}\)

\(\Rightarrow D=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+......+\frac{1}{2}.\left(\frac{1}{29}-\frac{1}{31}\right)\)

\(\Rightarrow D=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{31}\right)\)

\(\Rightarrow D=\frac{1}{2}.\frac{28}{93}=\frac{14}{94}\)

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