Using the limit comparison test


by hivesaeed4
Tags: comparison, limit, test
hivesaeed4
hivesaeed4 is offline
#1
Apr2-12, 10:26 PM
P: 217
I'm given the following:
3/(n(2^(n-1)))
I have to determine convergence using the limit comparison test. I've proved its convergent using the ratio test but am struggling with which term do I divide the above for the limit comparison test. Help?
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hivesaeed4
hivesaeed4 is offline
#2
Apr2-12, 10:31 PM
P: 217
Don't bother replying. I figured it out.
hivesaeed4
hivesaeed4 is offline
#3
Apr2-12, 10:34 PM
P: 217
I have just one question. Suppose the limit comparison test evaluates to infinity. Would it still prove convergence?

DonAntonio
DonAntonio is offline
#4
Apr3-12, 06:43 AM
P: 606

Using the limit comparison test


Quote Quote by hivesaeed4 View Post
I have just one question. Suppose the limit comparison test evaluates to infinity. Would it still prove convergence?

Either you're asking something else or you're confusing the limit comparison test: this test tells you that if the limit of the quotient of two positive sequences exists finitely and is NOT zero, then the series whose general term is one of the seq's converges iff the series whose general term is the other seq. converges...so what's your question?

DonAntonio
hivesaeed4
hivesaeed4 is offline
#5
Apr3-12, 09:25 AM
P: 217
Sorry. I should have been clearer. The question was if the limit comparison test evaluates to infinity and we used a series whose general term was known to be convergent then the series whose general term's convergence we have to determine, is it also convergent. You answered that question by stating the finite part. Thanks


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