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Sum of sequences

  1. Nov 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the sum of the sequence:
    2, -2/3, 2/9, -2/27, 2/81, . . .

    2. Relevant equations



    3. The attempt at a solution

    I can see that the number is multiplied by -1/3, but I'm unsure of how to find the sum.

    Any pointers?
     
  2. jcsd
  3. Nov 19, 2012 #2
    use the formula for the sum of geometric sequence.
     
  4. Nov 19, 2012 #3

    Mark44

    Staff: Mentor

    This is a geometric sequence. There's a formula for finding the sum of a geometric series.
     
  5. Nov 19, 2012 #4
    an+1-1/a-1
     
  6. Nov 19, 2012 #5
    Summed over n: [itex]\sum[/itex]ak=an+1-1/a-1
     
  7. Nov 19, 2012 #6

    Mark44

    Staff: Mentor

    Use parentheses!

    What you wrote is an + 1 - (1/a) - 1
     
  8. Nov 19, 2012 #7
    haha good note, your right. I have bad habits when it comes to those things
     
  9. Nov 19, 2012 #8
    Thanks for the help!

    I came up with 1 41/81 using the formula. This also equals the sum of the numbers in the sequence (in my original post).

    So, I guess it's correct.
     
  10. Nov 19, 2012 #9
    Although, this is in infinite geometric set so should I be using this formula:

    S∞ = a1/(1-r), where a1 = the first term in the sequence, and r is the ratio.
     
    Last edited: Nov 19, 2012
  11. Nov 19, 2012 #10
    So the answer would be 1 1/2. Correct?
     
  12. Nov 19, 2012 #11

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, it's 3/2.
     
  13. Nov 19, 2012 #12
    Thanks for the reassurance.
     
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