an是首项为3,公差,公差为2的等差数列,则lim(1/a1a2+1/a2a3+……+1/a(n-1)an)=

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an=3+2(n-1)=2n+1
lim[1/(a1a2)+1/(a2a3)+...+1/(a(n-1)an)]
=lim(1/2)[1/3-1/5+1/5-/7+...+1/(2n-1)-1/(2n+1)]
=lim(1/2)[1/3-1/(2n+1)]
n->∞,1/(2n+1)->0
lim[1/(a1a2)+1/(a2a3)+...+1/(a(n-1)an)]=1/6

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