<s>[INST] Finding the limit of $(\root 3 \of {{n^3} + {n^2}} - \root 3 \of {{n^3} + 1} )$ Any Ideas/Hints?  
$$\lim\limits_{n \to \infty } (\root 3 \of {{n^3} + {n^2}}  - \root 3 \of {{n^3} + 1} )$$
 [/INST] Hint: $a^3-b^3=(a-b)(a^2+ab+b^2)$. Take $a=\sqrt[3]{n^3+n^2}$ and $b=\sqrt[3]{n^3+1}$.
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