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silvermane
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Prove using the definition of a limit, Please help! :)
Prove using only the definition of a limit, that the sequence:
[tex]\frac{n}{(n+1)^1/2}[/tex] - [tex]\frac{n}{(n+2)^1/2}[/tex] converges.
Let E>0 and choose a special N = something*E that whenever n>N our difference of limits is less than E...
I know that the limit is 0, but I'm having trouble finding the special N. The algebra for this is horrible and I've spent a long while working on it. Please help. It will be greatly appreciated.
Homework Statement
Prove using only the definition of a limit, that the sequence:
[tex]\frac{n}{(n+1)^1/2}[/tex] - [tex]\frac{n}{(n+2)^1/2}[/tex] converges.
Homework Equations
Let E>0 and choose a special N = something*E that whenever n>N our difference of limits is less than E...
The Attempt at a Solution
I know that the limit is 0, but I'm having trouble finding the special N. The algebra for this is horrible and I've spent a long while working on it. Please help. It will be greatly appreciated.
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