What is the limit as n approaches infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n) ?

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limit as n approaches infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n)

n \to \infty lim (i = 1 \sum n (1 + \frac{2 i}{n})^{3} (\frac{2}{n}))

20

Solution steps

n \to \infty lim (i = 1 \sum n (1 + \frac{2 i}{n})^{3} (\frac{2}{n}))

Apply the limit of sum formula:

\int_{0}^{2} (1 + x)^{3} d x

Solve

\int_{0}^{2} (1 + x)^{3} d x : 20

= 20

What is the limit as n approaches infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n) ?
The limit as n approaches infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n) is 20