Question

求lim(n趋于无穷大)(1/n²+n+1 +2/n²+n+2 …+n/n²+n+n)

求lim(n趋于无穷大)(1/n²+n+1 +2/n²+n+2 …+n/n²+n+n)高数，求步骤

Answer 1

(1/(n²+n+1)+2/(n²+n+1)+ …+n/(n²+n+1))>(1/(n²+n+1)+2/(n²+n+2)+ …+n/(n²+n+n))>(1/(n²+n+n)+2/(n²+n+n)+ …+n/(n²+n+n))，而后由夹逼准则可得1/2>lim>1/2，故极限=1/2