Cho biết giá trị của (lim (sqrt {{n^2} + 2n}  – sqrt[3]{{{n^3} + 2{n^2}}})) bằng ?

(begin{array}{l}lim left( {sqrt {{n^2} + 2n}  – sqrt[3]{{{n^3} + 2{n^2}}}} right)\ = lim left( {sqrt {{n^2} + 2n}  – n} right) \+ lim left( {n – sqrt[3]{{{n^3} + 2{n^2}}}} right)\ = lim dfrac{{{n^2} + 2n – {n^2}}}{{sqrt {{n^2} + 2n}  + n}} \+ lim dfrac{{{n^3} – {n^3} – 2{n^2}}}{{{n^2} + n.sqrt[3]{{{n^3} + 2{n^2}}} + {{left( {sqrt[3]{{{n^3} + 2{n^2}}}} right)}^2}}}\ = lim dfrac{{2n}}{{sqrt {{n^2} + 2n}  + n}} \+ lim dfrac{{ – 2{n^2}}}{{{n^2} + n.sqrt[3]{{{n^3} + 2{n^2}}} + {{left( {sqrt[3]{{{n^3} + 2{n^2}}}} right)}^2}}}\ = lim dfrac{2}{{sqrt {1 + dfrac{2}{n}}  + 1}} \+ lim dfrac{{ – 2}}{{1 + sqrt[3]{{1 + dfrac{2}{n}}} + {{left( {sqrt[3]{{1 + dfrac{2}{n}}}} right)}^2}}}\ = 1 + left( { – dfrac{2}{3}} right) = dfrac{1}{3}end{array})