aleciapusey
9

# can anyone help??? Identify whether the series below is a convergent or divergent geometric series and find the sum, if possible.

$\sum\limits^{\infty}_{i = 1}{8(\frac{5}{6})^{i - 1}} = 8(\frac{5}{6})^{1 - 1} + 8(\frac{5}{6})^{2 - 1} + 8(\frac{5}{6})^{3 - 1} +...$ $\sum\limits^{\infty}_{i = 1}{8(\frac{5}{6})^{i - 1}} = 8(\frac{5}{6})^{0} + 8(\frac{5}{6})^{1} + 8\frac{5}{6})^{2} +...$ $\sum\limits^{\infty}_{i = 1} = 8(1) + 8(\frac{5}{6}) + 8(\frac{25}{36})+...$ $\sum\limits^{\infty}_{i = 1} = 8 + 6\frac{2}{3} + 5\frac{5}{9} +...$ $\sum\limits^{\infty}_{i = 1} = 20\frac{2}{9} +...$ The series is a divergent geometric series.