[tex]a = 2( \frac{1}{1 \times 3} + \frac{1}{3 \times 5} + ... + \frac{1}{27 \times 29} ) \times \frac{29}{14} = \frac{29}{7} ( \frac{1}{1} - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + ... + \frac{1}{27} - \frac{1}{29} ) = \frac{29}{7} (1 - \frac{1}{29} ) = \frac{29}{7} \times \frac{29 - 1}{29} = 4[/tex]
