Question

Help please!

Does the series converge or diverge? If it converges, what is the sum?
(infinity)
sigma -4(-(1/2))^(n-1)
n-1

Answer 1

it's a geometric series with the common ratio = -1/2. what does that tell you?

Answer 2

each number in the sequence is *-.5 from the last

Answer 3

ok, so how do you know if the series converges or diverges?

Answer 4

I don't recall.

Answer 5

if |r| < 1, then the series converges. Otherwise, diverges

Answer 6

So it converges?

Answer 7

is |-1/2| < 1?

Answer 8

Yes, but it's to the power of n-1, and multiplied by -4

Answer 9

-4 is irrelevant. it's the common ratio that determines whether a geometric series converges or diverges

Answer 10

okay, so it converges because -0.5<1

Answer 11

so, it converges because |-1/2| < 1

Answer 12

How do I find the sum if it uses infinity, though?

Answer 13

do you know the formula?

Answer 14

I think I do.

Answer 15

ok what is it?

Answer 16

x(n)=ar^(n-1)

Answer 17

no, it's

sum = (first term) / (1 - common ratio)

Answer 18

X=n/1=-0.5

Answer 19

ok

Answer 20

sum = -4/(1 - (-1/2))

do them math

Answer 21

-(8/3)?

Answer 22

yea

Answer 23

Is that the sum?

Answer 24

yea

Answer 25

Alright, thanks!

Answer 26

np