Question

Evaluate the series 8 + 4 + 2 + . . .

Answer 1

Answer:

16

Step-by-step explanation:

a/(1-r)

Use the infinite geometric series formula.

Answer 2

ANSWER

$S_{\infty} = 16$

EXPLANATION

Given the series:

8 + 4 + 2 + . . .

The first term of the series is

$a_1 = 8$

The common ratio is

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

The sum of this series is given by

$S_{\infty} = \frac{a_1}{1 - r}$

$S_{\infty} = \frac{8}{1 - \frac{1}{2} }$

Simplify:

$S_{\infty} = \frac{8}{\frac{1}{2} } = 8 \times 2 = 16$