lim(n→∞) [(x+a)/(x-2a)]^x
=lim(n→∞) [(1+a/x)/(1-2a/x)]^x
=lim(n→∞) (1+a/x)^x / (1-2a/x)^x
=lim(n→∞) [(1+a/x)^(x/a)]^a / [(1-2a/x)^(-x/2a)]^(-2a)
=e^a / e^(-2a)
=e^(-3a)
=27
所以,-3a=ln(27)=3ln3,所以a=-ln3
lim(n→∞) [(x+a)/(x-2a)]^x
=lim(n→∞) [(1+a/x)/(1-2a/x)]^x
=lim(n→∞) (1+a/x)^x / (1-2a/x)^x
=lim(n→∞) [(1+a/x)^(x/a)]^a / [(1-2a/x)^(-x/2a)]^(-2a)
=e^a / e^(-2a)
=e^(-3a)
=27
所以,-3a=ln(27)=3ln3,所以a=-ln3