Find the sum to infinity of the series 1 2 1 6 ... - JAMB Mathematics 2004 Question

\(a=\frac{1}{2}\r=\frac{\frac{1}{6}}{\frac{1}{2}}=\frac{1}{6}\times\frac{2}{1}=\frac{1}{3}\S_n = \frac{a}{1-r}\S_n = \frac{\frac{1}{2}}{1-\frac{1}{3}}\=\frac{\frac{1}{2}}{\frac{3}{2}}\=\frac{1}{2}\times\frac{3}{2}\=\frac{3}{4}\)