# How to show convergence of a sequence?

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Thread starter 5 years ago
#1
I have this question and other similar ones and I'm getting stuck.

Does

converge?

If so find the limit.

I am having real trouble with these types of questions I know about the sandwich theorem and trying to show is unbounded therefore divergent but I'm very bad.

Please help.
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5 years ago
#2
Have you come across algebra of limits? This may prove to be useful
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Thread starter 5 years ago
#3
(Original post by Slowbro93)
Have you come across algebra of limits? This may prove to be useful

Then dividing the fractions on both sides (top and bottom) by and applying the AOL for sums products and quotients we get.

and so

Is this right?
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5 years ago
#4
(Original post by poorform)
I have this question and other similar ones and I'm getting stuck.

Does

converge?

If so find the limit.

I am having real trouble with these types of questions I know about the sandwich theorem and trying to show is unbounded therefore divergent but I'm very bad.

Please help.

From the point of a "method mathematician" and not a purist

if you divide top and bottom by n2

then you get terms of O(1/n) and O(1/n2) which tend to zero as n tends to infinity

the limit is 1
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5 years ago
#5
(Original post by TeeEm)
From the point of a "method mathematician" and not a purist

if you divide top and bottom by n2

then you get terms of O(1/n) and O(1/n2) which tend to zero as n tends to infinity

the limit is 1
These questions are (almost) universally expected to be done from a "first principles" pure point of view, in which case that isn't going to be acceptable. (Although it would be perfectly acceptable in a pure course at postgrad level ironically).
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5 years ago
#6
(Original post by poorform)

Then dividing the fractions on both sides (top and bottom) by and applying the AOL for sums products and quotients we get.

and so

Is this right?
Yes that's fine.
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5 years ago
#7
(Original post by DFranklin)
These questions are (almost) universally expected to be done from a "first principles" pure point of view, in which case that isn't going to be acceptable. (Although it would be perfectly acceptable in a pure course at postgrad level ironically).
I have no idea what is expected but I suspected that might have been the case.
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