Re: Mathematical Question

[John W. Eaton]

On  2-Aug-2004, Ada Cheng <address@hidden> wrote:

| You can write (1-x^c)=(1-x)(1+x+...+x^{c-1}), this allows you to rewrite
| y as (sum_{k=1}^c x^k-x^c)/(1-x^c). y is clearly now in indeterminate
| form as x approaches 1.  Apply L'Hopital rule, do some algebra and you
| should get the answer.  (to make life easy on yourself, you will want to
| use finite sum of arithmetic series formula).
| 
| Hope this help.

And at least Maxima thinks your result is the right one:

  $ maxima
  GCL (GNU Common Lisp)  2.6.2 CLtL1   Jun 29 2004 18:53:13
  Source License: LGPL(gcl,gmp), GPL(unexec,bfd)
  Binary License:  GPL due to GPL'ed components: (READLINE BFD UNEXEC)
  Modifications of this banner must retain notice of a compatible license
  Dedicated to the memory of W. Schelter

  Use (help) to get some basic information on how to use GCL.
  Maxima restarted.
  (C1) limit (x/(1-x)-c*x^c/(1-x^c), x, 1);

                                       C - 1
  (D1)                                 -----
                                         2

jwe



-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
Subscription information:  http://www.octave.org/archive.html
-------------------------------------------------------------