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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
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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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can simply take values or take the limit as x > infinity^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the limit as x>infinite is zero, which is inconclusive

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no no, it means that the series converge ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you end up with zero, it means the series is converging :) and when you end up with infinity it diverges

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the series will not necessarily converge when the limit of the sequence as n>infinite is zero, for example 1/n

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry sstarica, that is not correct

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i was thinking limit comparison or ratio

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but ratio yields "1", inconclusive.. and not sure what converging or diverging series to limit compare to

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Simplifying a bit will help here..\[(n*2^n)/(2^n + 3^n) = n/[1 + (3/2)^n]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, I did that. not sure what the next steps are ... l'hopitals rule says the limit goes to zero

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0perhaps a comparison of some sort?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this question was driving me mad and I'm a tutor lol!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You tried the ratio test?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0converge. 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
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