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Help with a Geometric progression.

  1. Apr 17, 2005 #1
    I need a little help with this problem.

    In a geometric progession, the first term is 12 and the fourth term is -3/2. Find the sum to n terms and the sum to infinity. Find also, the least value of n for which the magnitude of the difference between the sum to infinity and to n terms are less than 0.001.

    I have first expressed the GP as,

    [tex] 12, T_2, T_3, -3/2 [/tex]

    I see that the ratio between the 4th and 1st terms is [tex] -\frac{1}{8} [/tex] and this is 3 times the common ration r, which is -1/24. To find the sum to n terms, i get,

    [tex] S_n =\frac {12 ( - \frac {1}{24} ^n -1 )}{-1/24-1} [/tex]

    and the sum to infinity is 11.52. However the sum to infinity is given as 8 in the answer.

    To find the last part of the question, i did,

    [tex] 11.52- \frac {12 ( - \frac {1}{24} ^n -1 )}{-1/24-1} = 0.001 [/tex] but it didn't work out to get the answer or n=13.

    Thanks alot for your help.
     
  2. jcsd
  3. Apr 17, 2005 #2
    Are you sure thats correct?
     
  4. Apr 17, 2005 #3
    OHHH ! it should be

    [tex] r^3 = -\frac {1}{8} [/tex]. thanks alot. that should settle it.

    edit:

    I have found the sum to infinity already and got 8. But have difficulty in the last part where they asked me to find the value of n where the difference between [tex] S_n [/tex] and [tex] S_\infty [/tex] is 0.001

    can someone help?
     
    Last edited: Apr 17, 2005
  5. Apr 17, 2005 #4
    I dont remember series very well, but I'm surethey offer a great explanation in your textbook. I remember ours had 3 pages to this cause alone.

    but as far as I can remember, you set [itex]S_n [/itex] to an errorestimation variable [itex] \epsilon[/itex], then set [itex]S_{\infty} -\epsilon < 0.001 [/tex] and I think you try solvin for n or something like that. Someone else probably has a better answer.
     
  6. Apr 17, 2005 #5

    OlderDan

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    The equation for [tex] S_\infty [/tex] comes from the equation for [tex] S_n [/tex] by taking the limit as n goes to infinity. Take the difference between the equations for [tex] S_\infty [/tex] and [tex] S_n [/tex] and set it equal to 0.001
     
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