问题 选择题
等差数列{an},{bn}的前n项和分别为Sn与Tn,若
Sn
Tn
=
2n
3n+1
,则
lim
n→∞
an
bn
等于(  )
A.1B.
6
3
C.
2
3
D.
4
9
答案

an
bn
=
2an
2bn
=
a1+a2n-1
b1+b2n-1
=
(2n-1)(a1+a2n-1
2
(2n-1)(b1+b2n-1
2
=
s2n-1
T2n-1

lim
n→∞
an
bn
lim
n→∞
s2n-1
T2n-1
=
lim
n→∞
2n-1
3n-1
=
2
3

故选C

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