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mathew0135 Group Title

Check whether the series defined below is convergent and if so, find its sum.

  • one year ago
  • one year ago

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  1. mathew0135 Group Title
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    \[\sum_{n=1}^{\infty} \frac{ 2^n }{ (-12)^{n-1} }\] and the equation.

    • one year ago
  2. zordoloom Group Title
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    What math class is this for?

    • one year ago
  3. etemplin Group Title
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    likely calc 2, because i just had a test on this

    • one year ago
  4. zordoloom Group Title
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    BTW, this series converges.

    • one year ago
  5. mathew0135 Group Title
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    Math 1B in Australia (presumably similar to calc 2 from what i've seen).

    • one year ago
  6. zordoloom Group Title
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    ok, the sum will also be -12/5

    • one year ago
  7. mathew0135 Group Title
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    thanks, good to know but how do you work that out?

    • one year ago
  8. zordoloom Group Title
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    Take the limit as n goes to infinity.

    • one year ago
  9. mathew0135 Group Title
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    thus far i've found the absolute value, then tried to find the limit as it approaches infinity. That's what i believe you do.

    • one year ago
  10. zordoloom Group Title
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    Ya. That would be correct. So, the form is an+1/an

    • one year ago
  11. zordoloom Group Title
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    And you plug in the formula that you have into this equation.

    • one year ago
  12. zordoloom Group Title
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    -(2^n+1)/(12^(n+1)(-1)) all over (2^n)/(-12^(n-1))

    • one year ago
  13. mathew0135 Group Title
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    okay so because the is to a higher power the limit is equal to 0 and thus converges. Hate to ask but how do you find the sum. Think you tried to explain it there but i'm still a bit confused. does: (-(2^n+1)/(12^(n+1)(-1)))/((2^n)/(-12^(n-1))) find me the sum when n=1?

    • one year ago
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