Question

Find the sum of the infinite geometric series, if it exists.


1/2 -2+ 8 -...

Answer 1

see any pattern ?

Answer 2

1/2

-2

8

what next ?

Answer 3

times -4?

Answer 4

Yes!

Answer 5

here's my answer choices...

Answer 6

a.-8192
b.1/10
c.32,768
d.does not exist

Answer 7

so the common ratio is \(-4\)
what do you know about the condition for convergence of geometric series ?

Answer 8

off of the top of my head, nothing. im overwhlemed so thanks for your patience.

Answer 9

so d is my answer? because if its not. what am i missing or doing wrong?

Answer 10

Notice that the terms itself are alternating and blowing up :

1/2

-2

8

-32

128

..... .

so intuitively it appears that the sum must not converge, that is the sum `does not exist`

Answer 11

ok i see. thank you!

Answer 12

if you look up ur notes, im sure you will find a nice criterian for convergence of geometric series

Answer 13

we aren't using a book. just worksheets with formulas on them.

Answer 14

thank you, i really appreciate your help.

Answer 15

http://seriestestmjs.weebly.com/uploads/1/1/5/7/11577982/2663460_orig.jpg That might help you :)

Answer 16

@Jhannybean thanks love! i appreciate it!

Answer 17

Here is the test for geometric series :

If the common ratio is between -1 and 1, then the sum converges, otherwise the sum doesn't converge.

Answer 18

@ganeshie8 ok i see, i see.

Answer 19

goes wid the caption ;)