Check for convergence or divergence in the following sequences?
just tell me which test to use
Currently both come up inconclusive (#L=1# ) with the Root Test ?
#a_n=(1+3/n)^(4n)#
#a_n=(n/(n+3))^n#
just tell me which test to use
Currently both come up inconclusive (
#a_n=(1+3/n)^(4n)# #a_n=(n/(n+3))^n#
A) Converges to
The Ratio and Root Tests are used for determining the behavior of infinite series rather than infinite sequences. Here, they won't really be of use.
Checking the convergence or divergence of a sequence is much simpler, and only requires taking the limit to infinity of the sequence.
A) Here, if we take the limit, we see
As a result, we're going to want to use l'Hospital's Rule.
Simplify the argument of the logarithm:
Take the limit to infinity:
This is definitely indeterminate, so differentiate the numerator and denominator:
So, we get
So, proceed as we did in the previous problem:
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Certainly! Please provide the sequences you'd like me to check for convergence or divergence.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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