# Convergence of 1/(x_n) if x_n is convergentWatch

#1
Question: If is a convergent real sequence with limit , where . Show that is convergent with limit

Would it be valid to write the following?

For to be convergent with limit we must have that .

Suppose that we define then so .

Thus we have that .

As required.

I feel slightly uneasy about dividing by . Is this allowed?

Any help is appreciated
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1 year ago
#2
You write "Suppose that we define delta ..." but I'm at a loss to what you think this *does*? Certainly defining it isn't enough to decide that |x_n - L| is less than it.
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#3
(Original post by DFranklin)
You write "Suppose that we define delta ..." but I'm at a loss to what you think this *does*? Certainly defining it isn't enough to decide that |x_n - L| is less than it.
I have just realised this is terribly unclear. I don't really know what I meant by it. Here is hopefully a more clear (attempted) explanation.

For to be convergent with limit we must have that .

Suppose that then .

Thus we have that .
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1 year ago
#4
You can't suppose the thing your supposing. (I'm kind of puzzled how you thought you *could* suppose it).
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1 year ago
#5
Should there not be the requirement that .

isn't good enough.
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1 year ago
#6
(Original post by Cryptokyo)
Suppose that .
Under what premises are you certain that this is true?
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1 year ago
#7
(Original post by ghostwalker)
Should there not be the requirement that .

isn't good enough.
Good point.
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