21: After substituting in the limit point you should find that
the expression is of the type
∞ − ∞.
The leading
term under the root is n3, 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".
Intuitive calculations
would make this leading term disappear,
![](gif5/eca5au1.gif)
so factoring out would not help.
Instead the best bet seems to be getting rid of the cubic root
algebraically, see the box
"difference of roots".
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