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MathGroup Archive 2005

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Re: Limit of list

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57479] Re: Limit of list
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Sun, 29 May 2005 01:03:38 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 5/28/05 at 5:39 AM, guyi1 at netvision.net.il (Guy Israeli) wrote:

>Is there a way to find out the convergence point of a list of
>numbers?

In general, no. The problem is there are literally an infinite number of ways to continue any finite list of numbers. For example, consider

{1,2,3 ...}

n + (n-1)(n-2)(n-3)f[n]

for any arbitrary function f will have the same first three numbers. More complicated schemes can be imagnined. All I need to reproduce the first three numbers is to arrange for additive term to have zeros for n = 1,2,3. So by choosing the function appropriately, I can make it converge or diverge as I want.

>for example if I have

>{1,2,5,6,8,9,10,11,10,11,12,11,12.. and so on}

If I assume the pattern displayed by the last four numbers persists, then the sequence doesn't converge.

>it will give me something around 10-12
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