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From: Merciadri Luca on 29 May 2010 08:25
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Hi,

It is sometimes interesting not to have to use Abel's theorem, or
Quotient's and Root's criteria, but to know, electronically, if a
serie (of function, or not), converge, and, if so, the value to which
it converges. Can it be done with the HP 50g? Implementing these
methods on it should be straightforward, as it uses

* basic calculus notions: limits, comparison criteria;
* basic algebra notions: decomposition into simple els., solving
* (in)equations with absolute values (for absolute convergence),

and all these features are already implemented on the HP
50g. Evidently, finding the value to which a serie converges is not
always feasible, but when it is feasible (say for trivial series, such
as those which simply need indices modifications, and decomposition in
simple els.) for an human, the HP50g should do it.

This might be very useful, because such series (of function or not,
simple numeric series) sometimes arise in practice, say e.g. from Taylor's
infinite developments.

Thanks.
- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
- --

When I was born, I was so surprised I didn't talk for a year and a
half. (Gracie Allen)
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From: supergems on 30 May 2010 16:13
On 29 Mag, 14:25, Merciadri Luca <Luca.Mercia...(a)student.ulg.ac.be>
wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Hi,
>
> It is sometimes interesting not to have to use Abel's theorem, or
> Quotient's and Root's criteria, but to know, electronically, if a
> serie (of function, or not), converge, and, if so, the value to which
> it converges. Can it be done with the HP 50g? Implementing these
> methods on it should be straightforward, as it uses
>
> * basic calculus notions: limits, comparison criteria;
> * basic algebra notions: decomposition into simple els., solving
> * (in)equations with absolute values (for absolute convergence),
>
> and all these features are already implemented on the HP
> 50g. Evidently, finding the value to which a serie converges is not
> always feasible, but when it is feasible (say for trivial series, such
> as those which simply need indices modifications, and decomposition in
> simple els.) for an human, the HP50g should do it.
>
> This might be very useful, because such series (of function or not,
> simple numeric series) sometimes arise in practice, say e.g. from Taylor's
> infinite developments.
>
> Thanks.
> - --
> Merciadri Luca
> Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/
> - --
>
>  When I was born, I was so surprised I didn't talk for a year and a
>  half. (Gracie Allen)
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.9 (GNU/Linux)
> Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/>
>
> iEYEARECAAYFAkwBB9EACgkQM0LLzLt8MhwZHgCgpukck/FW8NYRbIQCgDSwW5ds
> /vAAnRgz7d1rTRIPA1b3BmGv1oUJWYB3
> =1Y8k
> -----END PGP SIGNATURE-----

Hi Luca, you read

Sequences, Series and Limits Marathon
http://www.hpcalc.org/details.php?id=5290

and all marathon books
http://www.hpcalc.org/search.php?query=marathon

supergems
From: mjc on 30 May 2010 17:51
On May 30, 1:13 pm, supergems <simone.cer...(a)gmail.com> wrote:
> On 29 Mag, 14:25, Merciadri Luca <Luca.Mercia...(a)student.ulg.ac.be>
> wrote:
>
>
>
> > -----BEGIN PGP SIGNED MESSAGE-----
> > Hash: SHA1
>
> > Hi,
>
> > It is sometimes interesting not to have to use Abel's theorem, or
> > Quotient's and Root's criteria, but to know, electronically, if a
> > serie (of function, or not), converge, and, if so, the value to which
> > it converges. Can it be done with the HP 50g? Implementing these
> > methods on it should be straightforward, as it uses
>
> > * basic calculus notions: limits, comparison criteria;
> > * basic algebra notions: decomposition into simple els., solving
> > * (in)equations with absolute values (for absolute convergence),
>
> > and all these features are already implemented on the HP
> > 50g. Evidently, finding the value to which a serie converges is not
> > always feasible, but when it is feasible (say for trivial series, such
> > as those which simply need indices modifications, and decomposition in
> > simple els.) for an human, the HP50g should do it.
>
> > This might be very useful, because such series (of function or not,
> > simple numeric series) sometimes arise in practice, say e.g. from Taylor's
> > infinite developments.
>
> > Thanks.
> > - --
> > Merciadri Luca
> > Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/
> > - --
>
> >  When I was born, I was so surprised I didn't talk for a year and a
> >  half. (Gracie Allen)
> > -----BEGIN PGP SIGNATURE-----
> > Version: GnuPG v1.4.9 (GNU/Linux)
> > Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/>
>
> > iEYEARECAAYFAkwBB9EACgkQM0LLzLt8MhwZHgCgpukck/FW8NYRbIQCgDSwW5ds
> > /vAAnRgz7d1rTRIPA1b3BmGv1oUJWYB3
> > =1Y8k
> > -----END PGP SIGNATURE-----
>
> Hi Luca, you read
>
> Sequences, Series and Limits Marathonhttp://www.hpcalc.org/details.php?id=5290
>
> and all marathon bookshttp://www.hpcalc.org/search.php?query=marathon
>
> supergems

You might also try Aitken extrapolation (and it's cousin Steffenson
(sp?)).
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