lim(n趋向无穷)(n/(n^2+1^2)+n/(n^2+2^2+.n/(n^2+n^2)表示为定积分最好有详尽过程,不要只是个答案
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![lim(n趋向无穷)(n/(n^2+1^2)+n/(n^2+2^2+.n/(n^2+n^2)表示为定积分最好有详尽过程,不要只是个答案](/uploads/image/z/5435517-21-7.jpg?t=lim%EF%BC%88n%E8%B6%8B%E5%90%91%E6%97%A0%E7%A9%B7%EF%BC%89%EF%BC%88n%2F%28n%5E2%2B1%5E2%29%2Bn%2F%28n%5E2%2B2%5E2%2B.n%2F%28n%5E2%2Bn%5E2%29%E8%A1%A8%E7%A4%BA%E4%B8%BA%E5%AE%9A%E7%A7%AF%E5%88%86%E6%9C%80%E5%A5%BD%E6%9C%89%E8%AF%A6%E5%B0%BD%E8%BF%87%E7%A8%8B%EF%BC%8C%E4%B8%8D%E8%A6%81%E5%8F%AA%E6%98%AF%E4%B8%AA%E7%AD%94%E6%A1%88)
lim(n趋向无穷)(n/(n^2+1^2)+n/(n^2+2^2+.n/(n^2+n^2)表示为定积分最好有详尽过程,不要只是个答案
lim(n趋向无穷)(n/(n^2+1^2)+n/(n^2+2^2+.n/(n^2+n^2)
表示为定积分
最好有详尽过程,不要只是个答案
lim(n趋向无穷)(n/(n^2+1^2)+n/(n^2+2^2+.n/(n^2+n^2)表示为定积分最好有详尽过程,不要只是个答案
原式=lim(n->∞){(1/n)[n²/(n²+1²)+n²/(n²+2²)+.+n²/(n²+n²)]}
=lim(n->∞){(1/n)[1/(1+(1/n)²)+1/(1+(2/n)²)+.+1/(1+(n/n)²)]}
=∫(0,1)dx/(1+x²) (由定积分定义得)
=(arctanx)|(0,1)
=π/4-0
=π/4
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