Riemann Sum Q1

Riemann Sum Q1

7 marks

By considering the graph of \(y=\sqrt{x}\) for \(0\le x\le 1\), prove that \(\mathop{\lim}\limits_{n\to \infty }\,\frac{\sum\limits_{k=1}^{n}{\sqrt{k}}}{n\sqrt{n}}=\frac{2}{3}\).[7]

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Answer:\({\frac{2}{3}}\)

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