Question

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

Answer 1

16

Explanation:

a/(1-r)

Use the infinite geometric series formula.

Answer 2

`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 = (4)/(8) = (1)/(2)`

The sum of this series is given by

`S_(\infty) = (a_1)/(1 - r)`

`S_(\infty) = (8)/(1 - (1)/(2) )`

Simplify:

`S_(\infty) = (8)/((1)/(2) ) = 8 * 2 = 16`