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Question Number 97987 by abdomathmax last updated on 10/Jun/20

$$\mathrm{find}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}\sum _{\mathrm{k}=1}^{\mathrm{n}}\sqrt{\frac{\mathrm{n}-\mathrm{k}}{{\mathrm{n}}^3-{\mathrm{n}}^2\mathrm{k}}}$$

Answered by maths mind last updated on 11/Jun/20

$$=\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}\sum _{k⩽n}\sqrt{\frac{1}{n^2}\left(\frac{n-k}{n-k}\right)}$$$$=\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}.\sum _{k⩽n}\frac{1}{n}=\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}=0$$

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