Evaluate the limit by first recognizing the sum as the Riemann sum for a function defined on the interval [0,1]: lim as n approaches infinity (1/n)((sqrt(1/n)+(sqrt(2/n)+(sqrt(3/n)+...............+(sqrt(n/n))

Question

Evaluate the limit by first recognizing the sum as the Riemann sum for a function defined on the interval [0,1]:  lim as n approaches infinity (1/n)((sqrt(1/n)+(sqrt(2/n)+(sqrt(3/n)+...............+(sqrt(n/n))

anonymous · Answer

i have no idea how to start this question

zarkon · Answer

$$\int\limits_{0}^{1}\sqrt{x}dx$$

anonymous · Answer

would i have to use reimann sums to get the answer right?
Or just to to find the function

anonymous · Answer

(1/n)((sqrt(1/n)+(sqrt(2/n)+(sqrt(3/n)+...............+(sqrt(n/n))
$$(1/n)*\sum_{1}^{n}\sqrt[2]{(i/n)}=0.6667$$

anonymous · Answer

$$(1/n)[\sqrt{(1/n)}+\sqrt{(2/n)}+\sqrt{(3/n)}+...+\sqrt{(n/n)}=0.66667$$

anonymous · Answer

$$\int\limits_{0}^{1}\sqrt{x} dx=0.66666667=2/3$$