lim[1/(n^2+1)+2/(n^2+2)+....+n/(n^2+n)] n趋于无穷 怎么做
lim[1/(n^2+1)+2/(n^2+2)+....+n/(n^2+n)]n趋于无穷怎么做...
lim[1/(n^2+1)+2/(n^2+2)+....+n/(n^2+n)] n趋于无穷 怎么做
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设[1/(n^2+1)+2/(n^2+2)+....+n/(n^2+n)]=S则S<[1/(n^2+1)+2/(n^2+1)+....+n/(n^2+1)]=(1+2+……+n)/(n^2+1)=n*(n+1)/2(n^2+1)有因为S>[1/(n^2+n)+2/(n^2+n)+....+n/(n^2+1)]=n*(n+1)/2(n^2+n)且limn*(n+1)/2(n^2+1)=1/2(n趋于无穷)limn*(n+1)/2(n^2+n)=1/2(n趋于无穷)由夹逼原理知lim[1/(n^2+1)+2/(n^2+2)+....+n/(n^2+n)]
n趋于无穷=1/2
n趋于无穷=1/2
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