1/10 1/40 1/8 .... 1/(3x 2)(3x )=33/70

Lời giải:

\(\frac{1}{{2.5}} + \frac{1}{{5.8}} + \frac{1}{{8.11}} + ... + \frac{1}{{\left( {3{\rm{x}} + 2} \right)\left( {3{\rm{x}} + 5} \right)}} = \frac{4}{{25}}\)

\(\frac{1}{3}\left( {\frac{1}{2} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + ... + \frac{1}{{3{\rm{x}} + 2}} - \frac{1}{{3{\rm{x + 5}}}}} \right) = \frac{4}{{25}}\)

\(\frac{1}{3}\left( {\frac{1}{2} - \frac{1}{{3{\rm{x}} + 5}}} \right) = \frac{4}{{25}}\)

\(\frac{1}{2} - \frac{1}{{3{\rm{x}} + 5}} = \frac{{12}}{{25}}\)

\(\frac{1}{{3{\rm{x}} + 5}} = \frac{1}{{50}}\)

\(3{\rm{x}} + 5 = 50\)

\(x = 15\)