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Calculating Limit of Series – A third root minus a third root – Exercise 598

Exercise

Find the limit

\lim _ { n \rightarrow \infty}n^\frac{2}{3} (\sqrt[3]{n+1}-\sqrt[3]{n})

Final Answer


\lim _ { n \rightarrow \infty}n^\frac{2}{3} (\sqrt[3]{n+1}-\sqrt[3]{n}) = \frac{1}{3}

Solution

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