2: The problem is of the type ∞ − ∞. The leading term under the root is n², so when the root is taken into account, the first term behaves like n when n goes to infinity, that is, it is of the same order as the second term "-n". In intuitive calculations the leading terms cancel out

so we know that factoring out would not help.

Instead you would like to cancel n somehow. The best bet seems to be getting rid of the square root algebraically, see the box "difference of roots".

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