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# showing that a sequence converges - help watch

1. solved
2. Are you sure you can just square it? Wouldn't it be better to just keep it as sqrt( n/(n+1) )?

Were you not writing a delta-epsilon, I would mention that n=(n+1)-(1).

But I really have no idea how to do these formal proof thingies
3. (Original post by Kaya_01)
I need to show that this sequence Attachment 203242 converges as n tends to infinity.

I know I have to use the fact that abs(a_n - L) < e (e being epsilon)

I've started off by removing the square root by squaring the expression. I now have n/(n+1). What is the limit for this?

My proof is starting with stating with the fact that e > 0

Any help is hugely hugely appreciated! thank you!

As so that is it will be smaller and smaller
and

that is convergent
4. (Original post by ztibor)

As so
and

that is convergent
hey there - thank you so so much!!

can I ask what the purpose of rationalizing this expression is?
5. As someone else has said, you can't simply square it without knowing that is continuous for all of , because that's the only way you can square it and conclude the convergence implies the convergence of
6. (Original post by ztibor)

As so that is it will be smaller and smaller
and

that is convergent
Good explanation!

(i`d used that the sequence equals:

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