12.2 #11

Is this geometric series convergent? If so, what is its sum?

3+2+\frac{4}{3}+\frac{8}{9}...

The ratio between each value, r, is 2/3. Since |r|<1, this series converges. Although not asked to find it, the starting value a is 3.

To calculate the sum:
s=\frac{a}{1-r} = \frac{3}{1-\frac{2}{3}} = \frac{3}{1/3} = 9