Question

Đã trả lời bởi chuyên gia

Answer 1

Ta có:

$\frac{3}{35} + \frac{3}{63} + \frac{3}{99} + . . . + \frac{3}{x . (x + 2)} = \frac{24}{35} \frac{3}{5.7} + \frac{3}{7.9} + \frac{3}{9.11} + . . . + \frac{3}{x . (x + 2)} = \frac{24}{35} \frac{3}{2} . [\frac{2}{5.7} + \frac{2}{7.9} + \frac{2}{9.11} + . . . + \frac{2}{x . (x + 2)}] = \frac{24}{35} \frac{3}{2} . (\frac{1}{5} - \frac{1}{7} + \frac{1}{7} - \frac{1}{9} + \frac{1}{9} - \frac{1}{11} + . . . + \frac{1}{x} - \frac{1}{x + 2}) = \frac{24}{35} \frac{3}{2} . (\frac{1}{5} - \frac{1}{x + 2}) = \frac{24}{35} \frac{1}{5} - \frac{1}{x + 2} = \frac{24}{35} \div \frac{3}{2} \frac{1}{5} - \frac{1}{x + 2} = \frac{16}{35} \frac{1}{x + 2} = \frac{1}{5} - \frac{16}{35} \frac{1}{x + 2} = \frac{- 9}{35} x + 2 = \frac{- 35}{9} x = \frac{- 35}{9} - 2 x = \frac{- 53}{9}$

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Answer 2

Ta có:

$\frac{3}{35} + \frac{3}{63} + \frac{3}{99} + . . . + \frac{3}{x . (x + 2)} = \frac{24}{35} \frac{3}{5.7} + \frac{3}{7.9} + \frac{3}{9.11} + . . . + \frac{3}{x . (x + 2)} = \frac{24}{35} \frac{3}{2} . [\frac{2}{5.7} + \frac{2}{7.9} + \frac{2}{9.11} + . . . + \frac{2}{x . (x + 2)}] = \frac{24}{35} \frac{3}{2} . (\frac{1}{5} - \frac{1}{7} + \frac{1}{7} - \frac{1}{9} + \frac{1}{9} - \frac{1}{11} + . . . + \frac{1}{x} - \frac{1}{x + 2}) = \frac{24}{35} \frac{3}{2} . (\frac{1}{5} - \frac{1}{x + 2}) = \frac{24}{35} \frac{1}{5} - \frac{1}{x + 2} = \frac{24}{35} \div \frac{3}{2} \frac{1}{5} - \frac{1}{x + 2} = \frac{16}{35} \frac{1}{x + 2} = \frac{1}{5} - \frac{16}{35} \frac{1}{x + 2} = \frac{- 9}{35} x + 2 = \frac{- 35}{9} x = \frac{- 35}{9} - 2 x = \frac{- 53}{9}$

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