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 Jan 4 awarded Nice Question Jan 10 awarded Announcer Jun 28 comment Proof that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$? OK. I understand now. Jun 28 comment Proof that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$? $(n+1)^3 = \sum_{k=0}^n (k+1)^3 - k^3$ ? $(n+1)^3 = \sum_{k=0}^n (k+1)^3 - \sum_{k=0}^n k^3$ Jun 27 awarded Supporter Jun 27 comment Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$ @Beni Bogosel: If you understand Chinese, you can see link. In fact, I have asked on link. Sorry, I am a Chinese. My English is not very good. Jun 27 awarded Scholar Jun 27 comment Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$ @TonyK: This problem and Diophantine approximation theory are related. I never studied the Diophantine approximation theory, so to ask next. Jun 27 accepted Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$ Jun 27 comment Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$ @mac:I am a Chinese, my English is not very good. If you understand Chinese, you can see link. Thank you. Jun 27 comment Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$ @mac:Let $F=\sqrt[x]{|\sin x|}$, if $x=2k\pi$, $F=0$. If $x=(2k+1/2)\pi$, $F=1$. So $\lim_{x \to \infty} \sqrt[x]{|\sin x|}$ does not exist. Jun 27 awarded Student Jun 27 revised Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$ edited tags Jun 27 asked Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$ Jun 27 awarded Autobiographer