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Question Number 186853 by liuxinnan last updated on 11/Feb/23

$$lim(k\to \mathrm{\infty })\underset{i=1}{\sum ^k}\frac{1}{\sqrt{ki}}=?$$

Answered by Ar Brandon last updated on 11/Feb/23

$$\mathcal{L}=\underset{k\to \mathrm{\infty }}{\lim }\underset{i=1}{\sum ^k}\frac{1}{\sqrt{ki}}=\underset{k\to \mathrm{\infty }}{\lim }\frac{1}{k}\underset{i=1}{\sum ^k}\sqrt{\frac{k}{i}}$$$$={\int }_0^1\frac{1}{\sqrt{x}}dx=2{\left[\sqrt{x}\right]}_0^1=2$$

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