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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



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