求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方

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求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方

求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方
求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方
求极限:
当n→无穷,
1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?
注:n2=n的平方

求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方求极限:当n→无穷,1/(n2+n+1)+2/(n2+n+2)+……+n/(n2+n+n)等于?注:n2=n的平方
1/2.用夹逼定理.
该等式肯定小于1+2+.+n/n2+n+1.分母变小了.即把所有分母换成第一项的分母,分子不变.
同时肯定大于1+2+.+n/n2+n+n.分母变大了.即把所有分母换成最后一项的分母,分子不变.
但是二者的极限都是1/2.所以最后结果为1/2.

求极限:当n→无穷,1/(n^2+n+1)+2/(n^2+n+2)+...+n/(n^2+n+n)等于?
极限:当n→无穷,
1/(n^2+n+1)+2/(n^2+n+2)+...+n/(n^2+n+n)
≤1/(n^2+n+1)+2/(n^2+n+1)+...+n/(n^2+n+1)
=(1+2+...+n)/(n^2+n+1)
=(1/2)(n+1)n/...

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求极限:当n→无穷,1/(n^2+n+1)+2/(n^2+n+2)+...+n/(n^2+n+n)等于?
极限:当n→无穷,
1/(n^2+n+1)+2/(n^2+n+2)+...+n/(n^2+n+n)
≤1/(n^2+n+1)+2/(n^2+n+1)+...+n/(n^2+n+1)
=(1+2+...+n)/(n^2+n+1)
=(1/2)(n+1)n/(n^2+n+1)
-> 1/2
1/(n^2+n+1)+2/(n^2+n+2)+...+n/(n^2+n+n)
≥1/(n^2+n+n)+2/(n^2+n+n)+...+n/(n^2+n+n)
= (1+2+...+n)/[(n^2)+2n]
= (1/2)(n+1)n/[(n^2)+2n]
-> 1/2
所以,
当n→无穷,1/(n^2+n+1)+2/(n^2+n+2)+...+n/(n^2+n+n)
=1/2

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