Question

Tính A = 3/35+3/63+3/99+...+3/3599

 

Answer 1

Ta có A = \(\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{59.61}\right)\)

        A = \(\frac{2}{3}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{59}-\frac{1}{61}\right)\)

        A = \(\frac{2}{3}\cdot\left(\frac{1}{5}-\frac{1}{61}\right)\)

       A = \(\frac{2}{3}\cdot\left(\frac{61}{305}-\frac{5}{305}\right)\)

       A =\(\frac{2}{3}.\frac{26}{305}\)

        A = \(\frac{52}{915}\)

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