Explanation

(b)
$\frac{3}{4.8} - \frac{3.5}{4.8.12} + \frac{3.5.7}{4.8.12.16} - ... + \frac{3}{4} - \frac{3}{4}$
$= 1 - \frac{1}{4} + \frac{1.3}{2.4.4} - \frac{1.3.5}{4.4.2.4.3} + ... - \frac{3}{4}$
$= \left\lbrack 1 + \frac{1}{1!}\left( - \frac{1}{4} \right) + \frac{1(1 + 2)}{2!}\left( - \frac{1}{4} \right)^{2} + \frac{1(1 + 2)(1 + 4)}{3!}\left( - \frac{1}{4} \right)^{3} + ... \right\rbrack - \frac{3}{4}$
$= \left( 1 - \frac{1}{4} \right)^{- 1/2} - \frac{3}{4} = \sqrt{\frac{2}{3}} - \frac{3}{4}$