若lim[(2n-1)an]=1 求lim(n*an)的值
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若lim[(2n-1)an]=1 求lim(n*an)的值
若lim[(2n-1)an]=1 求lim(n*an)的值
若lim[(2n-1)an]=1 求lim(n*an)的值
lim[(2n-1)an]
=lim{[(2n-1)/n]*n*an}
因为llim(2n-1)/n=2
所以
lim[(2n-1)an]=2lim(n*an)=1
推知:
lim(n*an)=1/2
由题意可知,lim(an)=0,那么lim[(2n-1)an]=lim(2n*an)-lim(an)=lim(2n*an)=2lim(n*an)=1,所以lim(an)=1/2
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