Question

Find the sum of the following geometric progression:

1, −1/2, 1/4, −1/8, ... to 9 terms;

Answer 1

Here, a = 1 and r = − \[\frac{1}{2}\] .

\[\therefore S_9 = a\left( \frac{1 - r^9}{1 - r} \right) \]

\[ = 1 \left( \frac{1 - \left( - \frac{1}{2} \right)^9}{1 - \left( - \frac{1}{2} \right)} \right) \]

\[ = \frac{1 - \left( - \frac{1}{512} \right)}{\frac{3}{2}}\]

\[ = \frac{\frac{513}{512}}{\frac{3}{2}}\]

\[ = \frac{513 \times 2}{512 \times 3}\]

\[ = \frac{171}{256}\]