LIM1+3+5+…+(2n+1)/n^+1

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LIM1+3+5+…+(2n+1)/n^+1LIM1+3+5+…+(2n+1)/n^+1LIM1+3+5+…+(2n+1)/n^+11+3+5+…+(2n+1)有n+1项所以=(1+2n+1)(n+1

LIM1+3+5+…+(2n+1)/n^+1
LIM1+3+5+…+(2n+1)/n^+1

LIM1+3+5+…+(2n+1)/n^+1
1+3+5+…+(2n+1)
有n+1项
所以=(1+2n+1)(n+1)/2=(n+1)^2
所以LIM1+3+5+…+(2n+1)/(n^2+1)
=(n+1)^2/(n^2+1)
=(n^2+2n+1)/(n^2+1)上下同除n^2
=[1+2*(1/n)+1/n^2]/(1+1/n^2)
n→∞
则1/n→0,1/n^2→0
所以极限=(1+2*0+0)/(1+0)=1

lim(n->无穷){1+3+5+…+(2n+1)}/(n^+1)
=lim(n->无穷)n(2n+2)/(n^2+1)
=lim(n->无穷)4/2
=2