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

The limit as n approaches infinity of \sum_{i=1}^nsqrt((2i)/n)*2/n is (4sqrt(2))/3

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

n \to \infty lim (i = 1 \sum n \frac{2 i}{n} \cdot \frac{2}{n})

\frac{4 2}{3}

Decimal Notation

1.88561 \dots

Solution steps

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

Apply the limit of sum formula:

\int_{0}^{2} x d x

Solve

\int_{0}^{2} x d x : \frac{4 2}{3}

= \frac{4 2}{3}

\frac{\partial}{\partial x} (\frac{1}{x + 2})

f (x) = 3 x - 4 x^{2}, (- 1, - 7)

\int 5 x x + 4 d x

\frac{d}{d x} ((1 - x)^{\frac{2}{3}})

n = 0 \sum \infty \frac{1}{3 ^{n} + 2}

What is the limit as n approaches infinity of \sum_{i=1}^nsqrt((2i)/n)*2/n ?
The limit as n approaches infinity of \sum_{i=1}^nsqrt((2i)/n)*2/n is (4sqrt(2))/3