### Home > CCA2 > Chapter Ch10 > Lesson 10.3.1 > Problem10-148

10-148.

Find the sum for each of these infinite geometric series if possible. If it is not possible, explain.

1. $8 + 4 + 2 + ...$

Find the common ratio.

$\frac{4}{8}=\frac{1}{2}$

$\frac{2}{4}=\frac{1}{2}$

Use the equation for an infinite geometric series:

$\displaystyle\sum_{n=1}^{\infty}ar^{n-1}=\frac{a}{1-r}$

$16$

1. $3 + 9 + 27 + 81 + ...$

See part (a).

Not possible. $r > 1$, and the terms keep increasing.