Limit mistake !!!



Hello!
This example illustrates that the function limit misleads:
(%i1) (4^n+1)/(2^(2*n));
(%o1) (4^n+1)/2^(2*n)
(%i2) limit(%, n, inf);
(%o2) inf
The answer isn't corect, why?

Greetings from Krakow, Poland
W.