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#### Alexmahone

##### Active member

- Jan 26, 2012

- 268

Let $a_n=\sqrt{1}+\sqrt{2}+\ldots+\sqrt{n}$. Prove $a_n\sim\frac{2}{3}n^{3/2}$; ie, the ratio has limit 1 as $n\to\infty$.

I have posted my unsuccessful attempt to use the squeeze theorem. How do I improve the upper bound?

View attachment 9

I have posted my unsuccessful attempt to use the squeeze theorem. How do I improve the upper bound?

View attachment 9

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