求极限Xn=n/(n^2+1)+n/(n^2+2)

求极限Xn=n/(n^2+1)+n/(n^2+2)+n/(n^2+3)+……+n/(n^2+n),

2个回答

n/(n^2+1)+n/(n^2+2)+n/(n^2+3)+……+n/(n^2+n)n/(n²+n)+n/(²+n)+.+n/(n²+n)
=n*n/(n²+n)
=n/(n+1)
因lim n²/(n²+1)=1 limn/(n+1)=1
根据夹逼定理,limXn=1

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