is the above sequence convergent? if so, what is the limit?
Last edited by Jhevon; Mar 14th 2009 at 10:35 PM.
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Originally Posted by twilightstr is the above sequence convergent? if so, what is the limit? it is convergent. Hint: now take the limit
is it infinity
Originally Posted by twilightstr is it infinity no (if it were, it wouldn't be convergent) Hint 2: you can use L'Hopital's rule to find the limit
Just as an alternative.. If you can use the fact that for , then notice that: And use squeeze theorem ..
jhevon, how would u take the limit
Originally Posted by twilightstr jhevon, how would u take the limit I told you. I would use L'Hopital's rule. o_O gives a nice alternative
yes. thats what i tried doing in the first place, but i think i did it incorrectly.
Originally Posted by twilightstr yes. thats what i tried doing in the first place, but i think i did it incorrectly. recall that, by L'Hopital's, i suppose it is the that is giving you trouble. what did you get for this?
Originally Posted by twilightstr yes. thats what i tried doing in the first place, but i think i did it incorrectly. We'll be glad to look for any errors, but you'll need to show the work you did. Please be complete. Thank you!
= [(ln3)3^x + (ln5)5^x]/(3^x + 5^x) as the limit goes to infinity. I really dont know what to do from there
Originally Posted by twilightstr = [(ln3)3^x + (ln5)5^x]/(3^x + 5^x) as the limit goes to infinity. I really dont know what to do from there well, after that, we're good. multiply by , the limit should seem obvious from there
since and as
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