如何证明3n+2/2n+1的极限等于3/2 n趋近于无穷大
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lim(3n+2)/(2n+1)
=lim[(3n+3/2)/2*(n+1/2) +1/2*(2n+1)]
=lim[3/2+1/(4n+2)]
=3/2+lim[1/(4n+2)]
n趋近于无穷大,lim[1/(4n+2)]=0
所以:n趋近于无穷大
lim(3n+2)/(2n+1)=3/2
或者:
lim (3n+2)/(2n+1)
=lim[(3+2/n)/(2+1/n)]
n趋近于无穷大 2/n和1/n均趋向于0
所以:
n趋近于无穷大
lim (3n+2)/(2n+1)
=lim[(3+2/n)/(2+1/n)]=3/2
=lim[(3n+3/2)/2*(n+1/2) +1/2*(2n+1)]
=lim[3/2+1/(4n+2)]
=3/2+lim[1/(4n+2)]
n趋近于无穷大,lim[1/(4n+2)]=0
所以:n趋近于无穷大
lim(3n+2)/(2n+1)=3/2
或者:
lim (3n+2)/(2n+1)
=lim[(3+2/n)/(2+1/n)]
n趋近于无穷大 2/n和1/n均趋向于0
所以:
n趋近于无穷大
lim (3n+2)/(2n+1)
=lim[(3+2/n)/(2+1/n)]=3/2
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