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解答

lim[(n^2+n)^(1/2)-n]
=lim[n(1+1/n)^(1/2)-1]
=lim n[(1+1/n)^(1//2)-1][(1+1/n)^(1/2)+1]/(1+1/n)^(1/2)+1
=lim 1/[(1+1/n)^(1/2)+1], n->infinite,1/n = 0
=>lim 1/[(1+1/n)^(1/2)+1]=1/2

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