设常数a≠12，则limn→∞ln[n−2na+1n(1−2a)]n=．

Question

设常数a≠(1)/(2)，则

lim

n→∞

ln[(n−2na+1)/(n(1−2a))]n=______．

Answer 1

∵[(n−2na+1)/(n(1−2a))]n=[1+(1)/(n(1−2a))]n(1−2a)•(1)/(1−2a)
∴

lim

n→∞

ln[(n(1−2a)+1)/(n(1−2a))]n=

lim

n→∞

ln[1+(1)/(n(1−2a))]n(1−2a)•(1)/(1−2a)=ln

lim

n→∞

[1+(1)/(n(1−2a))]n(1−2a)•(1)/(1−2a)=lne(1)/(1−2a)=(1)/(1−2a)