Timeline for Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2017 at 1:14 | comment | added | zwim | Yes, nice one :p | |
| Feb 18, 2017 at 1:14 | comment | added | Simply Beautiful Art | I'm not sure what you mean, but since the $n!$ is raised to a negative power, we must find an upper bound, which flips to a lower bound, which then provides what we need quite nicely. | |
| Feb 18, 2017 at 1:07 | history | edited | zwim | CC BY-SA 3.0 |
added 65 characters in body
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| Feb 18, 2017 at 1:02 | comment | added | Simply Beautiful Art | One may acquire exact inequalities by noting that:$$n!=\exp\left[\sum\ln(k)\right]\le\exp\left[\int\ln(x)\ dx\right]=e\sqrt n\left(\frac ne\right)^n$$ | |
| Feb 18, 2017 at 0:57 | history | answered | zwim | CC BY-SA 3.0 |