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

Exercise

Find the limit

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

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