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sammietaygreen

  • one year ago

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

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  1. sammietaygreen
    • one year ago
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  2. sammietaygreen
    • one year ago
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    I know it converges.

  3. anonymous
    • one year ago
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    Do you know how to write the first four terms?

  4. sammietaygreen
    • one year ago
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    No.. not sure

  5. Vocaloid
    • one year ago
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    this is a geometric series with |r| < 1, so it converges you don't even have to write out the first terms if you don't want to

  6. sammietaygreen
    • one year ago
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    yes, but how do I calculate the answer?

  7. Vocaloid
    • one year ago
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    Oh, right, it's asking for the sum, too the sum of a geometric sequence is S = a1/(1-r) where a1 is the first term and r is the common ratio

  8. sammietaygreen
    • one year ago
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    8/3?

  9. sammietaygreen
    • one year ago
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    I still don't completely understand. Sorry.

  10. Vocaloid
    • one year ago
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    not quite, r = -1/2

  11. Vocaloid
    • one year ago
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    a1 = -4(1/2)^0 = -4

  12. sammietaygreen
    • one year ago
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    Oh!! I think I get it now.

  13. sammietaygreen
    • one year ago
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    is it because it has 1/2 in the equation?

  14. Vocaloid
    • one year ago
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    well, sort of the general form of a geometric sequence is a1(r)^(n-1), so, yes, r = -1/2

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