问题
选择题
已知数列{an}是由正整数组成的数列,a1=4且满足lgan=lgan-1+lgb,其中b>3,n>1,且n∈N+,则
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答案
由已知得an=b•an-1,
∴{an}是以a1=4,公比为c的等比数列,则an=4•bn-1.
lim n→∞
=3n-1-an 3n-1+an lim n→∞ 3n-1-4•bn-1 3n-1 +4•bn-1
当b>3时,原式=lim n→∞ 3n-1-an 3n-1+an
=lim n→∞ 3n-1-4•bn-1 3n-1 +4•bn-1
=lim n→∞
=-1(
)n-1-43 b (
)n-1+43 b
故选A.