\displaystyle\sum_{k = 0}^{\infty} \frac{(-1)^k}{16^k k! (2k+3)!!} <\displaystyle\sum_{k = 0}^{\infty} \frac{1}{16^k k! (2k+3)!!} < \displaystyle\sum_{k = 0}^{\infty} \frac{1}{16^k} = 1.06667