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## Homework Statement

Find the asymptotic formula for

[tex]\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{3}+...+\sqrt{n}[/tex]

in the form of [tex]c \ast n^{\alpha}[/tex]

Identify c and alpha.

(Do NOT use the fundamental theorem of calculus)

## Homework Equations

Area under curve [tex]y = \sqrt{x}[/tex] in [0, 1]

is [tex]\frac{1}{n^{\frac{3}{2}}}\sum^{n}_{i=1}\sqrt{i}[/tex]

## The Attempt at a Solution

...I'm really not sure from where to start...

I know [tex]c = \frac{2}{3}[/tex] and [tex]\alpha = \frac{3}{2}[/tex], but do not know how to prove it.

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