数列极限证明有关问题令Un=(n-1)(2n-1)/6n^2 ▏Un-A ▏= ▏1-3n/6n^2 ▏= 1/2n ▏1-3n^2 ▏0 只要1/2n1/2ε 所以对于任意给的ε>0取正整数N=[1/2ε] 则当n>N时 恒有▏Un-1/3▏
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![数列极限证明有关问题令Un=(n-1)(2n-1)/6n^2 ▏Un-A ▏= ▏1-3n/6n^2 ▏= 1/2n ▏1-3n^2 ▏0 只要1/2n1/2ε 所以对于任意给的ε>0取正整数N=[1/2ε] 则当n>N时 恒有▏Un-1/3▏](/uploads/image/z/5457928-40-8.jpg?t=%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90%E8%AF%81%E6%98%8E%E6%9C%89%E5%85%B3%E9%97%AE%E9%A2%98%E4%BB%A4Un%3D%28n-1%29%282n-1%29%2F6n%5E2+%E2%96%8FUn-A+%E2%96%8F%3D+%E2%96%8F1-3n%2F6n%5E2+%E2%96%8F%3D+1%2F2n+%E2%96%8F1-3n%5E2+%E2%96%8F0+%E5%8F%AA%E8%A6%811%2F2n1%2F2%CE%B5+%E6%89%80%E4%BB%A5%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%BB%99%E7%9A%84%CE%B5%3E0%E5%8F%96%E6%AD%A3%E6%95%B4%E6%95%B0N%3D%5B1%2F2%CE%B5%5D+%E5%88%99%E5%BD%93n%3EN%E6%97%B6+%E6%81%92%E6%9C%89%E2%96%8FUn-1%2F3%E2%96%8F)
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