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anonymous

  • 5 years ago

Does this series converge or diverge? (n*2^n)/(2^n + 3^n) and by which test

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  1. anonymous
    • 5 years ago
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    you can simply take values or take the limit as x --> infinity^_^

  2. anonymous
    • 5 years ago
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    the limit as x-->infinite is zero, which is inconclusive

  3. anonymous
    • 5 years ago
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    no no, it means that the series converge ^_^

  4. anonymous
    • 5 years ago
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    when you end up with zero, it means the series is converging :) and when you end up with infinity it diverges

  5. anonymous
    • 5 years ago
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    the series will not necessarily converge when the limit of the sequence as n-->infinite is zero, for example 1/n

  6. anonymous
    • 5 years ago
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    Sorry sstarica, that is not correct

  7. anonymous
    • 5 years ago
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    I need another test

  8. anonymous
    • 5 years ago
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    prifk is right

  9. anonymous
    • 5 years ago
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    i was thinking limit comparison or ratio

  10. anonymous
    • 5 years ago
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    but ratio yields "1", inconclusive.. and not sure what converging or diverging series to limit compare to

  11. anonymous
    • 5 years ago
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    Simplifying a bit will help here..\[(n*2^n)/(2^n + 3^n) = n/[1 + (3/2)^n]\]

  12. anonymous
    • 5 years ago
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    yes, I did that. not sure what the next steps are ... l'hopitals rule says the limit goes to zero

  13. anonymous
    • 5 years ago
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    perhaps a comparison of some sort?

  14. anonymous
    • 5 years ago
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    this question was driving me mad and I'm a tutor lol!

  15. anonymous
    • 5 years ago
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    You tried the ratio test?

  16. anonymous
    • 5 years ago
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    yes. 1

  17. anonymous
    • 5 years ago
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    i'll try again

  18. anonymous
    • 5 years ago
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    yeah, still 1

  19. anonymous
    • 5 years ago
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    converge. Ask hinted by polpak, write (n*2^n)/(2^n + 3^n) as n/[1 + (3/2)^n]. Then compare this with n(2/3)^n which is convergent by the Ratio test

  20. anonymous
    • 5 years ago
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    Nice!

  21. anonymous
    • 5 years ago
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    well done! thank you

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