Question

Find the limit of the geometric series.
1+1/2+1/4+1/8 a. 1 b.0 c. 1/2 d. 2

Answer 1

2

Explanation:

S=1+1/2+1/4+1/8+...

Multiply both sides by 2:

2S=2+1+1/2+1/4+1/8+....

Subtract equations:

-1S=-2

Divide both sides by -1

S=2

Or you could just keep adding more terms of the series to see it is approaching 2.

1+1/2=3/2=1.5

1+1/2+1/4=1.75

1+1/2+1/4+1/8=1.875

And so on..