>>>>> "Stavros" == Stavros Macrakis <macrakis at alum.mit.edu> writes:
Stavros> Alas, limit does not handle radcan'ed expressions correctly in general either:
Stavros> ex: (6^n+5^n)/6^n
Stavros> limit(ex,n,inf) => 1 (OK)
Stavros> limit(radcan(ex),n,inf) => inf (Wrong!)
I have a fix for this particular bug. The basic issue is that
limit(5^n/(2^n*3^n),n,inf) is not quite handled correctly.
Limit uses a heuristics on the order of growth and it sees that 5^n is
exponential growth of order n*log(5). However, limit thinks that
2^n*3^n has exponential growth of order n*log(3), because ISMAX
computes the maximum growth of a product of terms. If the exponential
terms are combined into one and simplified, the exponential order of
growth becomes log(6)*n. Them limit can tell that the numerator grows
more slowly than the denominator and the limit is 0.
This doesn't solve the original issue with limit(4^n/(2^(2*n)),n,inf),
but as Stavros says, radcan takes care of that.
Ray