Hi all.
(I tried to send this to rwg@tc.spnet.com but it bounced.
This is welcome news!
Bill, where are you?)
As before, rwg@spnet.com. The spurious "From: rwg@tc.spnet.com" was due to a bug at my ISP. Then some homo defecans began sending tons of viral spam "From: rwg@tc.spnet.com", and I'm getting hundreds of 40KB angry bounces. I asked my ISP to block mail To: rwg@tc.spnet.com.
f[x_] := Sum[(-1)^(n-j) Binomial[j,n-j] x^(n-j),{j,1,n}] / Sum[(-1)^(n+2-j) Binomial[j,n+2-j] x^(n+2-j),{j,1,n+2}] produces a well known Generating Function for the limit n->Infinity.
Q: What is needed to force Limit[f[x], n->Infinity] into submission? it equals (1-2x - Sqrt[1 - 4*x]) / (2 x^2)
Mathematica's package Calculus`Limit` doesn't feel like tackling it. Should it?
Wouter.
Both Mma and Macsyma need a little help here. Just send the sum limits to infinity first. It might also help to start from j=0, which you may have intended. If not, Mma may need you to "manually" subtract the j=0 term. Then you can even start from j=-inf. The resulting sums are simple algebraics(n), and n->inf is a snap. --Bill PS, does anyone have an eaddress for Dan Weinreb?