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What is the sum of the series to 7 terms?

$\frac{1}{1.4} + \frac{1}{2.5} + \frac{1}{3.6} + ............. + \frac{1}{7.10} = \frac{1}{3} (1 - \frac{1}{4} + \frac{1}{2} - \frac{1}{5} + \frac{1}{3} - \frac{1}{6} + ............. + \frac{1}{7} - \frac{1}{10}) = \frac{1}{3} [1 - \frac{1}{4} + \frac{1}{2} - \frac{1}{5} + \frac{1}{3} - \frac{1}{6} + \frac{1}{4} - \frac{1}{7} + \frac{1}{5} - \frac{1}{8} + \frac{1}{6} - \frac{1}{9} + \frac{1}{7} - \frac{1}{10}] = \frac{1}{3} [1 + \frac{1}{2} + \frac{1}{3} - \frac{1}{8} - \frac{1}{9} - \frac{1}{10}] = \frac{1}{3} [\frac{11}{6} - \frac{121}{360}] = \frac{1}{3} \times \frac{539}{360} = \frac{539}{1080}$

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