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Question Number 68693 by Maclaurin Stickker last updated on 15/Sep/19

Commented by turbo msup by abdo last updated on 15/Sep/19

$$let{S}_n=\sum _{k=1}^n(\frac{1}{\sqrt{k}}-\frac{1}{\sqrt{k+1}})\Rightarrow$$$$S_n=1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}$$$$=1-\frac{1}{\sqrt{n+1}}\Rightarrow {lim}_{n\to +\mathrm{\infty }}{S}_n=1$$

Commented by Maclaurin Stickker last updated on 15/Sep/19

$$Fabulous.$$

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