Question 6
Evaluate the infinite series
$$1-\frac16+\frac{1\cdot3}{2!}\left(\frac16\right)^2-\frac{1\cdot3\cdot5}{3!}\left(\frac16\right)^3+\frac{1\cdot3\cdot5\cdot7}{4!}\left(\frac16\right)^4-\cdots.$$
$$1-\frac16+\frac{1\cdot3}{2!}\left(\frac16\right)^2-\frac{1\cdot3\cdot5}{3!}\left(\frac16\right)^3+\frac{1\cdot3\cdot5\cdot7}{4!}\left(\frac16\right)^4-\cdots.$$