anonymous
  • anonymous
Does this series converge or diverge? (n*2^n)/(2^n + 3^n) and by which test
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
you can simply take values or take the limit as x --> infinity^_^
anonymous
  • anonymous
the limit as x-->infinite is zero, which is inconclusive
anonymous
  • anonymous
no no, it means that the series converge ^_^

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anonymous
  • anonymous
when you end up with zero, it means the series is converging :) and when you end up with infinity it diverges
anonymous
  • anonymous
the series will not necessarily converge when the limit of the sequence as n-->infinite is zero, for example 1/n
anonymous
  • anonymous
Sorry sstarica, that is not correct
anonymous
  • anonymous
I need another test
anonymous
  • anonymous
prifk is right
anonymous
  • anonymous
i was thinking limit comparison or ratio
anonymous
  • anonymous
but ratio yields "1", inconclusive.. and not sure what converging or diverging series to limit compare to
anonymous
  • anonymous
Simplifying a bit will help here..\[(n*2^n)/(2^n + 3^n) = n/[1 + (3/2)^n]\]
anonymous
  • anonymous
yes, I did that. not sure what the next steps are ... l'hopitals rule says the limit goes to zero
anonymous
  • anonymous
perhaps a comparison of some sort?
anonymous
  • anonymous
this question was driving me mad and I'm a tutor lol!
anonymous
  • anonymous
You tried the ratio test?
anonymous
  • anonymous
yes. 1
anonymous
  • anonymous
i'll try again
anonymous
  • anonymous
yeah, still 1
anonymous
  • anonymous
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
anonymous
  • anonymous
Nice!
anonymous
  • anonymous
well done! thank you

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