Re: Bug in Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg96468] Re: [mg96426] Bug in Limit
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 14 Feb 2009 03:09:27 -0500 (EST)
- Reply-to: hanlonr at cox.net
You can confuse it into giving the right answer but the behavior is inconsistent.
expr1 = ((-1)^n*n)/((-1)^n*n + 1);
expr2 = expr1 // Apart
1 - 1/((-1)^n*n + 1)
expr3 = (Cos[n*Pi]*n)/(Cos[n*Pi]*n + 1);
Simplify[expr1 == expr3, Element[n, Integers]]
True
expr4 = expr3 // Apart
1 - 1/(n*Cos[Pi*n] + 1)
Limit[#, n -> Infinity] & /@ {expr1, expr2, expr3, expr4}
{0,0,1,1}
Limit[#, n -> Infinity] & /@ expr2
1
Limit[#, n -> Infinity] & /@ expr4
Limit[-(1/(n*Cos[Pi*n] + 1)),
n -> Infinity] + 1
(1 + Limit[# - 1, n -> Infinity]) & /@ {expr1, expr2, expr3, expr4}
{1, 1, Limit[(n*Cos[Pi*n])/
(n*Cos[Pi*n] + 1) - 1,
n -> Infinity] + 1,
Limit[-(1/(n*Cos[Pi*n] + 1)),
n -> Infinity] + 1}
Bob Hanlon
---- azzteke <klaus.giesselmann at web.de> wrote:
=============
In both V6 and V7 Limit[((-1)^n*n)/((-1)^n*n + 1), n -> Infinity]
gives 0 instead of 1.
Any idea?
Thanks
Klaus