Can the limit of (√(n^2+1) - n) be solved?

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SUMMARY

The limit lim n→∞ (√(n^2+1) - n) can be solved by multiplying by the conjugate, specifically (√(n^2+1) + n)/(√(n^2+1) + n). This technique simplifies the expression, allowing for easier evaluation as n approaches infinity. The discussion emphasizes that this method is straightforward and effective for this type of limit problem.

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Homework Statement



Solve the limit: lim n→∞ (√(n^2+1) - n)

Homework Equations





The Attempt at a Solution



I am very lost on how to start so I do not have anything
 
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Multiplying by 1 in the form of (sqrt(n^2+1)+n)/(sqrt(n^2+1)+n) is probably the easiest way to go. There's other ways to do it. Try that one first.
 
Have you tried multiplying by the conjugate?

edit: too slow.
 

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