Question

7/15 + 7/35 + 7/77 + .... + 7/6399

Answer 1

Ta có :

\(P=\dfrac{7}{15}+\dfrac{7}{35}+\dfrac{7}{77}+...+\dfrac{7}{6399}\)

\(=\dfrac{7}{3.5}+\dfrac{7}{5.7}+\dfrac{7}{7.11}+...+\dfrac{7}{79.81}\)

\(\Rightarrow\dfrac{2}{7}P=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.11}+...+\dfrac{2}{79.81}\)

\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{79}-\dfrac{1}{81}\)

\(=\dfrac{1}{3}-\dfrac{1}{81}=\dfrac{26}{81}\)

\(\Rightarrow P=\dfrac{26}{81}\div\dfrac{2}{7}=\dfrac{91}{81}\)