作业帮高数夹逼咋做
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高数夹逼咋做
高数夹逼咋做
高数夹逼咋做
∵1/(n^2+n)<1/(n^2+1)<1/n^2
1/(n^2+n)<1/(n^2+1)<1/n^2
.............................................
1/(n^2+n)=1/(n^2+n)<1/n^2
∴limn->∞ n[1/(n^2+1)+1/(n^2+2)+........+1/(n^2+n)]<
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∵1/(n^2+n)<1/(n^2+1)<1/n^2
1/(n^2+n)<1/(n^2+1)<1/n^2
.............................................
1/(n^2+n)=1/(n^2+n)<1/n^2
∴limn->∞ n[1/(n^2+1)+1/(n^2+2)+........+1/(n^2+n)]<
limn->∞ n[1/n^2+1/n^2+........+1/n^2]
=limn->∞n^2/n^2 =1
limn->∞ n[1/(n^2+1)+1/(n^2+2)+........+1/(n^2+n)]>
=limn->∞ n[1/(n^2+n)+1/(n^2+n)+........1/(n^2+n)]
=limn->∞n^2/(n^2+n)
=limn->∞ n/(n+1)
=1
∴limn->∞ n[1/(n^2+1)+1/(n^2+2)+........+1/(n^2+n)]=1
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