Question

Determine if the following series is convergent or divergent.

Answer 1

\[-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}+...\]

Answer 2

This is a geometric series with ratio -1/2
A geometric series converges if the ratio r between terms is -1 < r < 1, so this series converges.

Answer 3

Proof:

s = -1/2 + 1/4 - 1/8 + ...
-1/2s = 1/4 - 1/8 + 1/16 - ...

s - (-1/2)s = -1/2 + 1/4 - 1/4 + 1/8 - 1/8 +... = -1/2
s + 1/2 s = -1/2
3/2s = -1/2
s = -3

Answer 4

Thank you for your help :)

Answer 5

nooo the sum is -1/3

Answer 6

Oops, guy is right, the sum is -1/3. I divided wrong =(
However, the series is still convergent.

Answer 7

Okay, thank you