Explanation

(c)
Let $S = 1 + \frac{1}{2!} + \frac{1.3}{4!} + \frac{1.3.5}{6!} + ...\infty$
$\therefore T_{n} = \frac{1.3.5.\ldots.(2n - 1)}{(2n)!} \times \frac{2.4.\ldots.2n}{2.4.\ldots.2n}$
$= \frac{(2n)!}{(2n)!2^{n}(n)!} = \frac{1}{2^{n}(n)!}$
$\therefore S = 1 + \sum_{}^{}{T_{n} = 1 + \frac{1}{2(1)!} + \frac{1}{2^{2}(2)!} + ...\infty}$
$= e^{1/2} = \sqrt{e}$