What is a convergent sequence and a divergent sequence?
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Convergent, divergent, oscillating and alternating sequences, examples, exercises and problems with solutions.
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if sequence {an} is divergent and {bn} is convergent, is the squence {an-bn} divergent?
Answer:
Yes. If {(a-b)(n)} were also convergent, then since {a(n)} = {b(n)} + {(a-b)(n)} would also have to...
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(a) Determine whether the sequence a(subscript n)= (n!/(2^n)) , n > or = 1 is convergent or divergent. if it converges find its limit. (b) Let a(subscript 1) = 1 and a(subscript n) = (sqrt(2+a(subscript n) - 1)) for n > or = 2 Prove that the sequence...
Answer:
I'll do the first one for you. a) We see that: a_(n + 1) = (n + 1)!/2^(n + 1) a_n = n!/2^n Then: [a...
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Answer:
A convergent infinite geometric series is a series with infinite terms which converges to a sum, because...
Anonymous at ChaCha Mark as irrelevant Undo
I believe that it would be convergent by the alternating series test, but I am not certain. Can you please tell me if I am on the right track, I would greatly appreciate it! Also, I am somewhat confused on the limit part. Any hints or suggestions for...
Answer:
The sequence is bounded and it is a monotone sequence ("monotone" means either "only...
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I believe that it would be convergent by the alternating series test, but I am not certain. Can you please tell me if I am on the right track, I would greatly appreciate it! Also, I am somewhat confused on the limit part. Any hints or suggestions for...
Answer:
You are right, the leibniz test is adequate for the task: it alternates, and 1/(2n) is decreasing. As...
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Answer:
nth term of the sequence = (3n-1)! /(3n+1)! = (3n-1)! /(3n+1)(3n)(3n-1)! = 1/(3n)(3n-1) As n approaches...
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"If we apply a continuous function to the terms of a convergent sequence, the result is also convergent." -If lim (as n approaches infinity) of a "sub" n = L and ...show more
Answer:
Your examples are a bit different. For e^x, you don't have a convergent sequence to begin with if you...
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Answer:
If a sequence has a limit we say it is convergent. If not, we say it is divergent. The similarity of...
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