anonymous
  • anonymous
Find the sum of the infinite geometric series, if it exists. 1/2 -2+ 8 -...
Mathematics
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anonymous
  • anonymous
Find the sum of the infinite geometric series, if it exists. 1/2 -2+ 8 -...
Mathematics
jamiebookeater
  • jamiebookeater
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ganeshie8
  • ganeshie8
see any pattern ?
ganeshie8
  • ganeshie8
1/2 -2 8 what next ?
anonymous
  • anonymous
times -4?

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ganeshie8
  • ganeshie8
Yes!
anonymous
  • anonymous
here's my answer choices...
anonymous
  • anonymous
a.-8192 b.1/10 c.32,768 d.does not exist
ganeshie8
  • ganeshie8
so the common ratio is \(-4\) what do you know about the condition for convergence of geometric series ?
anonymous
  • anonymous
off of the top of my head, nothing. im overwhlemed so thanks for your patience.
anonymous
  • anonymous
so d is my answer? because if its not. what am i missing or doing wrong?
ganeshie8
  • ganeshie8
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`
anonymous
  • anonymous
ok i see. thank you!
ganeshie8
  • ganeshie8
if you look up ur notes, im sure you will find a nice criterian for convergence of geometric series
anonymous
  • anonymous
we aren't using a book. just worksheets with formulas on them.
anonymous
  • anonymous
thank you, i really appreciate your help.
Jhannybean
  • Jhannybean
http://seriestestmjs.weebly.com/uploads/1/1/5/7/11577982/2663460_orig.jpg That might help you :)
anonymous
  • anonymous
@Jhannybean thanks love! i appreciate it!
ganeshie8
  • ganeshie8
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.
anonymous
  • anonymous
@ganeshie8 ok i see, i see.
dan815
  • dan815
|dw:1439181519693:dw|
ganeshie8
  • ganeshie8
goes wid the caption ;) |dw:1439181598024:dw|

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